# Math Word Problems and Solutions - Distance, Speed, Time

**Problem 1**
A salesman sold twice as much pears in the afternoon than in the morning.
If he sold 360 kilograms of pears that day, how many
kilograms did he sell in the morning and how many in the afternoon?

**Problem 2** Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked
2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick?

**Problem 3**

Sophia finished $\frac{2}{3}$ of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?

**Problem 4**

A farming field can be ploughed by 6 tractors in 4 days. When 6 tractors work together, each of them ploughs
120 hectares a day. If two of the tractors were moved to another field,
then the remaining 4 tractors could plough the same field in 5 days.
How many hectares a day would one tractor plough then?

**Problem 5**

A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?

**Problem 6**

I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose?

**Problem 7**

The distance between two towns is 380 km. At the same moment, a passenger car and a truck start moving towards each other from
different towns. They meet 4 hours later. If the car drives 5 km/hr faster than the truck, what are their speeds?

**Problem 8**

One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle
will increase by 18 cm^{2}. Find the lengths of all sides.

**Problem 9**

The first year, two cows produced 8100 litres of milk. The second year their production increased
by 15% and 10% respectively, and the total amount of milk increased to
9100 litres a year. How many litres were milked from each cow each year?

**Problem 10**

The
distance between stations A and B is 148 km. An express train left station A towards station B with the speed of 80 km/hr. At the same
time, a freight train left station B towards station A with the speed of 36 km/hr. They met at station C at 12 pm, and by that time the
express train stopped at at intermediate station for 10 min and the freight train stopped for 5 min. Find:

a) The distance between stations C and B.

b) The time when the freight train left station B.

**Problem 11**

Susan drives from city A to city B. After two hours of driving she
noticed that she covered 80 km and calculated that, if she continued
driving at the same speed, she would end up been 15 minutes late. So
she increased her speed by 10 km/hr and she arrived at city B 36 minutes earlier
than she planned.

Find the distance between cities A and B.

**Problem 12**

To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3
days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced.
Find how many parts the company made and how many days this took.

**Problem 13**

There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3
roses, every three boys planted 1 birch. By the end of the day they planted $24$ plants. How many birches and roses were planted?

**Problem 14**

A car left town A towards town B driving at a speed of V = 32 km/hr. After 3 hours on the road the driver stopped for 15 min in town C. Because of a
closed road he had to change his route, making the trip 28 km longer. He increased his speed to V = 40 km/hr but still he was 30 min late. Find:

a) The distance the car has covered.

b) The time that took it to get from C to B.

**Problem 15**

If a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he
still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?

**Problem 16**

A woodworker normally makes a certain number of
parts in 24 days. But he was able to increase his productivity by 5 parts per day, and so he
not only finished the job in only 22 days but also he made 80 extra parts. How many parts does the
woodworker normally makes per day and how many pieces does he make in 24 days?

**Problem 17**

A biker covered half the distance between two towns in 2 hr 30 min.
After that he increased his speed by 2 km/hr. He covered the second half of the distance in 2 hr 20 min. Find the distance between the two towns
and the initial speed of the biker.

**Problem 18**

A train covered half of the distance between stations A and B at the speed of 48 km/hr, but then it had to stop for 15 min. To make up
for the delay, it increased its speed by $\frac{5}{3}$ m/sec and it arrived to station B on time.
Find the distance between the two stations and the speed of the train after the stop.

**Problem 19**

Elizabeth can get a certain job done in 15 days, and Tony can finish only 75% of
that job within the same time. Tony worked alone for several days and then Elizabeth joined him, so they finished the rest of
the job in 6 days, working together.

For how many days have each of them worked and what percentage of the job have each of them completed?

**Problem 20**

A farmer planned to plough a field by doing 120
hectares a day. After two days of work he increased his daily productivity by 25% and he finished the job two days ahead of schedule.

a) What is the area of the field?

b) In how many days did the farmer get the job done?

c) In how many days did the farmer plan to get the job done?

**Problem 21**

To mow a grass field a team of mowers planned to cover 15 hectares a day. After 4 working days they increased the daily productivity by
$33 \times \frac{1}{3}\%$, and finished the work 1 day earlier than it was planned.

A) What is the area of the grass field?

B) How many days did it take to mow the whole field?

C) How many days were scheduled initially for this job?

Hint**:** See problem 20 and solve by yourself.

**Answer:** A) 120 hectares; B) 7 days; C) 8 days.

**Problem 22**

A train travels from station A to station B. If the train leaves station A
and makes 75 km/hr, it arrives at station B 48 minutes ahead of scheduled. If it made 50 km/hr, then by the scheduled time of arrival it would
still have 40 km more to go to station B. Find:

A) The distance between the two stations;

B) The time it takes the train to travel from A to B according to the schedule;

C) The speed of the train when it's on schedule.

**Problem 23**

The distance between towns A and B is 300 km. One train departs from town A and another train departs from
town B, both leaving at the same moment of time and heading towards each other. We know that one of them is 10 km/hr faster than the other. Find
the speeds of both trains if 2 hours after their departure the distance between them is 40 km.

**Problem 24**

A bus travels from town A to town B. If the bus's speed is 50 km/hr, it will arrive in town B 42 min later than scheduled. If the bus increases
its speed by $\frac{50}{9}$ m/sec, it will arrive in town B 30 min earlier than scheduled. Find:

A) The distance between the two towns;

B) The bus's scheduled time of arrival in B;

C) The speed of the bus when it's on schedule.