6. A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B's speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
[spoiler]Ans: A[/spoiler]
Word Translation - help
This topic has expert replies
Case 1: when A wins by 1/10 of a minute time:
Distance covered by A = 480 m.
Distance covered by B = 480 - 48 = 432 m
Time taken by A = t1 sec
Time taken by B = t1 + (1/10 of a min= 1/10 *60=6) = (t1 + 6) sec
note: u have to find ans in m/s
Case 2: when B wins by 1/30 of a minute time
Distance covered by A = 480
Distance covered by B = (480 -144)= 336
Time taken by B = t2 sec
Time taken by A = t2 + (1/30 of a min= 1/30 *60=2) = t2+2 sec
Remember speed of A and B remain same in both cases, so equate above unknowns as:
Speed = Distance/ Time (in m/s)
Speed of A = 480/t1 = 480/(t2+2) [-> eqn 1]
Speed of B = 432/(t1 + 6) = 336/t2 [-> eqn 2]
-> from 1st eqn: t2+2 =t1,
replace t1 in eqn 2 with (t2+2)
432/(t2+2+6) = 336/t2
after solving this I got: t2=28 sec
Speed of B = 336/t2 = 336/28 = 12 m/s.
so A is the correct ans as per my knowledge and calculation.
Distance covered by A = 480 m.
Distance covered by B = 480 - 48 = 432 m
Time taken by A = t1 sec
Time taken by B = t1 + (1/10 of a min= 1/10 *60=6) = (t1 + 6) sec
note: u have to find ans in m/s
Case 2: when B wins by 1/30 of a minute time
Distance covered by A = 480
Distance covered by B = (480 -144)= 336
Time taken by B = t2 sec
Time taken by A = t2 + (1/30 of a min= 1/30 *60=2) = t2+2 sec
Remember speed of A and B remain same in both cases, so equate above unknowns as:
Speed = Distance/ Time (in m/s)
Speed of A = 480/t1 = 480/(t2+2) [-> eqn 1]
Speed of B = 432/(t1 + 6) = 336/t2 [-> eqn 2]
-> from 1st eqn: t2+2 =t1,
replace t1 in eqn 2 with (t2+2)
432/(t2+2+6) = 336/t2
after solving this I got: t2=28 sec
Speed of B = 336/t2 = 336/28 = 12 m/s.
so A is the correct ans as per my knowledge and calculation.
- kvcpk
- Legendary Member
- Posts: 1893
- Joined: Sun May 30, 2010 11:48 pm
- Thanked: 215 times
- Followed by:7 members
1/10th of minute = 6 secondsarjunsekhar wrote:6. A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B's speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
[spoiler]Ans: A[/spoiler]
1/30th of minute = 2 seconds.
When B got 48m head start, B was 6 seconds behind.
When B got 144m head start, B was 2 seconds ahead.
Which means, B travelled, (144-48)m in 6+2 = 8 seconds
=96m in 8 seconds
speed = 96/8 = 12m/sec
pick A.
Hope this helps!!
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)