Michael is 1.5 times as fast as Bob. If Michael gives a head start of

Question

Michael is 1.5 times as fast as Bob. If Michael gives a head start of 150 meters to Bob and the race ends in a tie, then what is the track length?

(A) 900 meter
(B) 800 meters
(C) 450 meters
(D) 300 meters 
(E) 150 meters

imeanup · Answer

$$
Speed = \dfrac{Distance}{Time} \
Speed
\begin{cases}
\propto Distance \ \propto \dfrac{1}{Time}
\end{cases}
$$

\dfrac{S_M}{S_B} = \dfrac{3}{2} = \dfrac{D_M}{D_B} , whereas M = Michael, and B = Bob

D_M - D_B = 3 - 2 = 1 \Longrightarrow 150   m

D_M = 3	imes 150=450  m ( Length of the track )

D_B=2 	imes 150=300   m

Ans C

CrackverbalGMAT · Answer

Let the length of the race track be = x m

Since the race ends in a tie, the time taken by Mike to run x m = Time taken by Bob to run x - 150 m

Time = Distance / Speed

Given that Mike is 1.5 times as fast as Bob

Therefore  \frac{x}{1.5 * S_B} = \frac{x - 150}{S_B}

x = 1.5 (x - 150)

1.5x - x = 225

0.5x = 225

x = 450 m

Option C

Arun Kumar

hk111 · Answer

Here we know that mike and bob took equal amount of time to complete the race

d = s*t
s = d/t

Speed (bob) = x ,then, Speed(mike) = 1.5x
Distance(bob) = y, then, Distance(mike) = y + 150

comparing time,

y+150/1.5x = y/x
y+150 = 1.5y
150 = 0.5y
y = 300 meters

so total track length = y + 150(head start given to bob)
Total track length = 450m

rishikasrivastava · Answer

Speed of A : Speed of B = 3 : 2
This question is an application of time = constant
The ratio their speeds is 3:2 ; therefore the ratio of distance covered by them will also be 3:2
Length of the race equals the distance traveled by A.
When the difference between distances is 1 , A traveled 3.
When the difference between distances is 150 meters , A will travel 3* 150 meters = 450

mcrea · Answer

rate Bob = x
rate Michael = (3/2)*x or 1.5x

track lenght is the distance ran by Michael

distance Michael = distance Bob + headstart
1.5x*t = x*t +150
x*t*(1.5-0.5) = 150
x*t=150/0.5 = 300 = distance of Bob
distance of Bob + headstart = 300+150=450

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Michael is 1.5 times as fast as Bob. If Michael gives a head start of

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