► Speed and Distance sums
1) An empty tank measuring 78 cm by 50 cm by 30 cm had a crack at the bottom. The crack caused water to flow out of the tank at a rate of 0.4 ℓ per min. The tank was placed under a running tap that would fill it with water at a rate of 1 ℓ per minute.
a) How long would it take for the empty tank to be 3⁄5 filled?
b) What percentage of the tank would be filled in half an hour's time?
Ans :- a) 117 min
b) 155⁄13 % .
2) The radius of bicycle wheel is 35 cm. How many revolutions does it need to make to cover a distance of 440 m? (Take π = 22⁄7)
Ans :- 200.
3) Pail A contained 20 litres of water at first. Pail B, which is empty, fills at a rate of 15 litres per minute for 4 minutes before the tap filling Pail A is turned on. Pail A fills at a rate of 11 litres per minute. Water is leaking from the bottom of Pail B at a rate of 1 litre per minute.
(a) How much water is in Pail B one minute after the tap filling Pail A is turned on?
(b) How long will it take for Pail B to contain 54 litres more water than pail A?
Ans :- a)75 ℓ
b) 7 ½ min.
4) Mr. Tan sends his son to school every morning at 6.15 a.m. If he drives at an average speed of 60 km/h, his son will be 10 minutes late for school. If he speeds at an average speed of 120 km/h, his son will arrive in school 10 minutes early. What should Mr. Tan's average speed be if he wants his son to arrive in school on time?
Ans :- 80 km/h.
5) Town A and Town B are 760 km apart. At 9.40 a.m., Gopal set off from Town A to Town B at a constant speed of 80 km/h. Half an hour later, Haron set off from Town B to Town A at a constant speed which is 10 km/h slower than Gopal's speed. What time will they meet each other along the way?
Ans :- They will meet at 2.58 pm.
6) A rectangular container, measuring 80cm by 50cm by 50cm, was filled with water to a depth of 40cm. The water was drained out for 14 minutes at a rate of 2ℓ per minute. What was the new height of the water level after 14 minutes?
Ans :- 33 cm.
7) Mr. Tok left Town A for Town B at 11.30 am. He travelled at an average speed of 75 km/h. At 12.15 pm, Ms. Selva left Town A for Town B, travelling on the same route at an average speed of 100 km/h.
(a) At what time would Ms. Selva overtake Mr. Tok?
(b) After Ms. Selva had overtaken Mr. Tok, she took another 2 hours to reach Town B. What was the distance between Town A and Town B?
Ans :- a) 2.30 pm
b) 425 km .
8) A car left Town X for Town Y at the same time when a motorcycle left Town Y for Town X. The average speed for the car is 88 km/h while the average speed of the motorcycle was 64 km/h. The two vehicles passed each other at a point 33 km from the midpoint between Town X and Town Y. What was the distance between Town X and Town Y?
Ans :- 418 km.
9) 3 square-based containers each of depth 5 cm were linked at the centres to form a fondue fountain as shown below. If the chocolate flowed from the 2-cm square-based column tube at a rate of 80 ml per minute, how long would it take to fill the three tiers completely?
Ans :- 28 minutes .
10) Mark and Nani were heading for their school from their homes. Mark started walking at a speed of 30 m/min. At 6.45 a.m., Mark passed Nani's flat and Nani started walking to the school at a certain speed. At 7 a.m., Nani was 150 m ahead of Mark.
a) Find the speed at which Nani was walking. [answer: 40 m/min]
b) If Nani reached the school 8 min ahead of Mark, at what time did Mark reach the school?
Ans :- 7.17 a.m.