► Speed and Distance sums
1) Station A and Station B were 109 km apart. At 7a.m., a bus left Station A and travelled to Station B at an average speed of 63 km/h. At the same time, a cyclist left Station B and cycled towards Station A at 18 km/h along the same road. How far apart were the bus and the cyclist at 7.40 a.m.?
Ans :- 55 km.
2) A swimmer was swimming slowly from a beach to a small island, without resting. For every 10 m he swims, he is pushed back by the waves for 1m . It takes him 4 seconds to swim towards the island and 1 second to be pushed back by 1 m.
(a) How far would the swimmer have swum after 1 minute?
(b) What is the shortest time the swimmer would take to reach the island 505 m away?
Ans :- a) 108m
b) 4 min 39 sec
3) A large wheel makes 6 revolutions in 5 seconds while a small wheel makes 18 revolutions in 3 seconds.
(a) How many revolutions would the large wheel make in 8 minutes if it moves at a constant speed?
(b) If the large wheel makes 216 revolutions, how many revolutions will the small wheel make if both wheels start turning at the same time and move at a constant speed?
Ans :- a) Large wheel would make 576 revolutions
b) Small wheel will make 60 revolutions.
4) Perry Town and Phi City are 540 km apart. At 08 00, a lorry starts travelling to Phi City from Perry Town at a constant speed of 52 km/h. At 09 00, a car leaves Phi City for Perry Town at a constant speed of 72 km/h.
(a) At what time will the car and the lorry be 240 km apart?
(b) After leaving Phi City for 4 hours, the car increases its speed to 84 km/h. At what time would the car reach Perry Town?
Ans :- a) At 11 00
b) At 16 00 or 4.00 p.m.
5) Tony and Charles took part in a car race. Tony drove at a speed of 90 km/h. Both of them did not change their speed throughout the race. When Charles had covered 1⁄3 of the distance, Tony was 15 km in fromt of him. Tony reached the finishing line at 9.35 am. At what time did Charles reach the finishing line?
Ans :- At 10.05 am Charles reach the finishing line.
6) Wynn started her journey with 24.4ℓ of petrol in her car's tank. After travelling for a distance, she found that she had only 4.2ℓ of petrol left in the tank. She refilled $40 worth of petrol at $0.80 per litre. She continued her journey and at the end of it, she had 8.8ℓ of petrol left. If 0.2ℓ of petrol is needed for every 1 km, find the total distance Wynn covered for that day.
Ans :- Wynn covered 328 km on that day.
7) There are 2 teams of workers at a fast food restaurant. Team G has 30 more members than Team H. Each member in Team G prepares 4 burgers per minute while each member of Team H prepares 3 burgers per minute. In 1 hour, both teams prepare 36 600 burgers altogether. How many members are there in each team?
Ans :- Team G has 100 and Team H has 70 members.
8) Tap A takes 5 minutes to fill ¼ of a tank. Tap B takes 10 minutes to fill up the same tank to its brim. If both Taps A and B are turned simultaneously, how long will it take to fill the tank completely? (Leave your answer as a fraction in the simplest form)
Ans :- It will take 62⁄3 min .
9) Gary and Edwin started off together in the same direction from Town A and drove towards Town B at an average speed of 60 km/h and 96 km/h respectively. How far apart would they be after 20 minutes?
Ans :- They would be 12 km apart.
10) A car and a lorry which were 80 km apart started to travel towards each other at the same time. The car was 40 km/h faster than the lorry. They went past each other after 2⁄5 hours.
(a) How far did the lorry travel when it passed the car?
(b) Find the speed of the lorry.
Ans :- a) Lorry travelled 32 km
b) The speed of the lorry is 80 km/h.
11) Toy A and Toy B started from Point X and moved in the opposite direction round a circular track. Toy A took 6 minutes to reach Point X again at a speed of 10 m/min while Toy B was still 6 m away from Point X.
(a) What was the speed of Toy B?
(b) If both of them continued moving and stopped only after having moved 9 minutes from the starting time, how far apart would they be?
Ans :- a) 9m/min
b) 9m .