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Numerical Ability
Time Distance and Speed
In a kilometre race, if A gives B a 40 m start, A wins by 19 s. But if A gives B a 30 s start, B wins by 40 m. Find the time taken by B to run 5,000 m?
a. 150 s
b. 450 s
c. 750 s
d. 825 s
Read Solution (Total 8)
-
- 750 secs
When B is given a 40 m start then B runs 960m in T secs and A runs 1000m in T-19 secs.
When B is given a 30 second start then B runs 1000m in t secs and A runs 960m in t - 30 secs.
Assume that the speed of A (Va) and B (Vb) is constant in both situations.
Then Vb = 960 ÷ T = 1000 ÷ t, and Va = 1000 ÷ (T - 19) = 960 ÷ (t - 30)
So 960t = 1000T, and 1000t - 30000 = 960T - 18240. Then 40t = -40T + 11760, t = -T + 294.
Substituting for t in 960t = 1000T
gives : -960T + 282240 = 1000T
1960T = 282240
T = 144
B 's speed is 960 / T = 960 / 144 = 6.67 metres per second.
Assuming the same constant speed to run 5000 metres then the time taken is
5000 / 6.67 = 750 seconds - 13 years agoHelpfull: Yes(67) No(18)
- 1)if A gives B a 40 m start, A wins by 19 :-
distance=while A runs 1000m,B runs 960m
time=A time is unknown;B takes 19s more than A to cover 960m
speed=Let 'a' be speed of A ; 'b' be the speed of B
Time=Distance/Speed
Time taken by A=1000/a;Time taken by B=960/b
from 1)=> 1000/a + 19 = 960/b
2)if A gives B a 30 s start, B wins by 40 m
while B runs 1000m , A runs 960m
B takes 30s more than A to cover the 1000m
Distance of A=1000m ; Distance of B=960m
Time taken by A and B is unknown.B takes 30s more than A
speed of A='a' ;B='b'
Time taken by A=960/a ; Time taken by B=1000/b
From 2)=>960/a + 30 = 1000/b
1)=> 1000/a = 960/b -19 ; 2) 960/a = 1000/b - 30
Divide 1/2 => 1000/960 = 960 - 19b / 1000 - 30b
25/24 = 960 - 19b / 1000 - 30b
25(1000 - 30b) = 24(960 - 19b)
solving,we get b=20/3
sub b in 1)
1000/a = 960/(20/3) - 19
a = 8
Time taken by b to cover 5000m = 5000/b
= 5000/(20/3)
= 750 seconds
- 10 years agoHelpfull: Yes(18) No(3)
- b. 750 s
EA gives B a 40metre start then B runs 960m in T secs and A runs 1000m in T-19 secs.
2.A gives B a 30 second start then B runs 1000m in t secs and A runs 960m in (t-30) secs.
Assuming speed of A=X and B=Y
Then
X = 960 ÷ T = 1000 ÷ t,
960t = 1000T
Y = 1000 ÷ (T - 19) = 960 ÷ (t - 30)
1000t - 30000 = 960T - 18240
Then 40t = -40T + 11760,
t = -T + 294.
Substituting for t in 960t = 1000T gives
-960T + 282240 = 1000T
1960T = 282240
T = 144
B 's speed is 960 ÷ T = 960 ÷ 144 = 6.67 metres per second.
to run 5000 metres the time taken is 5000 ÷ 6.67 = 750 seconds = 12 minutes 30 seconds - 13 years agoHelpfull: Yes(10) No(15)
- 750 s by the mathematical order.
- 13 years agoHelpfull: Yes(5) No(18)
- 750 s by the mathematical order.
- 10 years agoHelpfull: Yes(2) No(4)
- When B is given a 40metre start then B runs 960m in T secs and A runs 1000m in T-19 secs.
When B is given a 30 second start then B runs 1000m in t secs and A runs 960m in t - 30 secs.
Assume that the speed of A (Va) and B (Vb) is constant in both situations.
Then Vb = 960 ÷ T = 1000 ÷ t, and Va = 1000 ÷ (T - 19) = 960 ÷ (t - 30)
So 960t = 1000T, and 1000t - 30000 = 960T - 18240. Then 40t = -40T + 11760, t = -T + 294.
Substituting for t in 960t = 1000T gives : -960T + 282240 = 1000T : 1960T = 282240 : T = 144
B 's speed is 960 ÷ T = 960 ÷ 144 = 6.67 metres per second.
Assuming the same constant speed to run 5000 metres then the time taken is 5000 ÷ 6.67 = 750 seconds = 12 minutes 30 seconds. - 11 years agoHelpfull: Yes(1) No(5)
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- 1 year agoHelpfull: Yes(0) No(0)
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