11. In a race of 400m, A gave B a head start of 20m at the start of the race. B took 48 seconds to complete the race. What was the speed of A if B defeated A by a margin of 2 seconds ?
Sol:
time taken by B to complete race = 48 sec
∴ time taken by A to complete race = 48 + 2 = 50 sec and in this time distance travelled by A = 400 m
∴ Speed of A = \(\frac{{400}}{{50}}\) = 8m/sec Answer
12. In a 1500 m race, if vehicle A gives vehicle B a start of 200m, then vehicle A wins the race by 8 sec. Alternatively if vehicle A gives vehicle B a start of 400 m , the race ends in a dead heat. How long does vehicle A takes to run 1500 m ?
Sol:
13. A runs \(\frac{5}{2}\) times as fast as B. In a race, if A gives a lead of 40m to B, find the distance from the starting point where both of them will meet.
Sol:
Stop B & give its velocity to A by reversing direction.
∴ A & B will meet after \(\frac{{40}}{{5 – 2}}\) = \(\frac{{40}}{3}\) sec
distance of meeting point from A = \(\frac{{40}}{3}\) × speed of A
= \(\frac{{40}}{3}\) × 5
= 66.66 m Answer
14. A can run 1.8 m in the same time that B runs 2 m. In a 3 km race, find by how much distance B beats A.
Sol:
Clearly B wins. So he will reach end point first.
Time taken by B to reach end point = \(\frac{{3 \times 1000}}{2}\)
= 1500 unit
in the same time A will reach = 1500 × 1.8 = 2700m
∴ B beats A by 3000 – 2700 = 300m Answer
15. A and B run 1 km and A wins by 40 sec. A and C run 1 km and A wins by 200 metre. When B and C run the same distance B wins by 20 seconds. Find the time taken by A to run 1 km.
Sol:
∴ \(\frac{{800}}{t} = \frac{{1000}}{{t + 60}}\)
5t = 4t + 240
t = 240 sec = 4 min Answer
16. In a 100m race, A runs at 9 km/h. If A gives B a start of 10m and still beats him by 5 seconds, what is the speed of B ?
Sol:
Speed of A = 9 km/h = 9 × \(\frac{5}{{18}}\) m/sec
Time taken by A to complete race = \(\frac{{100}}{{2.5}}\) = 40 sec
∴ time taken by B = 40 + 5 = 45 sec
& distance covered = 100 – 10 = 90 m
∴ Speed of B = \(\frac{{90}}{{45}}\) = 2 m/sec = 2 × \(\frac{{18}}{{5}}\) = 7.2 km/h Answer
17. In a race of 1 km, A beats B by 200 m, while in another race of 2000 m, c beats D by 500 m. Speed of B is equal to that of D. If A & C participate in a race of 2880 m then by how much distance C will beat A.
Sol:
18. In a race of 1 km, A beats B by 120 m or 15 sec. If hey start a race of 1 km simultaneously from the same point and if B gets injured afeter running 100 m less than half the race length and due to which his speed becomes \({\frac{3}{4}^{th}}\) of his original speed then by how much time A beats B ?
Sol:
time taken by B in new condition = \(\frac{{500 – 100}}{{18}} + \frac{{600}}{{\frac{3}{4} \times 8}}\) = 50 + 100 = 150 sec
∴ A beats B by = 150 – 110 = 40sec Answer
19. In a 500 m race A runs at a speed of 14.4 km/h. He gives a start of 20m to and still defeats him by 35 sec. What is the speed of B ?
Sol:
14.4 km/h = 14.4 × \(\frac{5}{{18}}\) m/sec = 4 m/sec
Speed of A = 4 m/sec
Time taken by A = \(\frac{{500}}{4}\)
Time taken by B = 125 + 35 = 160 sec
& distance covered by B = 500 – 20 = 480 m
∴ Speed of B = \(\frac{{480}}{{160}}\) = 3 m/sec = 3 × \(\frac{{18}}{5}\) km/h
= 10.8 km/h Answer
20. A can run 112 m in 15 seconds and B in 21 seconds. How many metres start can A give to B in 1.4 km race so that the race end in a dead-heat.
Sol:
In second case race end in dead-heat. So time will be same for both A & B i.e. time is constant. So ratio of speed will be same as ratio of distance.