Karen places a bet with Tom that she will beat Tom in a car race by 4

Question

Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many miles will Tom drive before Karen wins the bet?

A. 15
B. 18
C. 21
D. 24
E. 27

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sumit99kr · Answer

Karen starts 4 minutes late means for initial 4mins only Tom will be moving and would have covered 45*(4/60) = 3 miles.

Also, at the end Tom will be 4miles behind Karen.

So the relative distance to be covered by Karen is (3+4) = 7miles.

Relative speed= (60-45) = 15mph.
Time taken to cover this 7miles= 7/15 hrs
In 7/15 hrs Tom should cover= (7/15) *45= 21miles
Initially Tom had covered 3miles, so total distance= 21+3=24miles.

D is the correct choice.

Thanks  gmatophobia  for providing correct solution.

An alternative simpler solution would be-
Let "t" hrs be the time for which Karens travels, so Tom would travel for t+4/60 = (t+1/15)hrs.

Now when Karen travels for "t" she creates a gap of 4miles.

So, the difference of distance travelled by Karen in "t" hrs and Tom in (t+1/15) hrs would be 4miles.

60t - 45(t+1/15) = 4
15t - 3 = 4
15t = 7
t= 7/15 (karens time) 
Tom travelled for t+1/15 = 7/15 + 1/15 = 8/15

So in 8/15 hrs Tom covers a distance = (8/15)*45 = 24 miles.

gmatophobia · Answer

Karen starts 4 minutes late, in that 4 minutes Tom has driven  \frac{4}{60} * 45   = 3 miles

To win the bet, Karen must cover the gap of 3 miles and should create a gap of 4 miles (she must travel 4 miles ahead of Tom). So Karen must travel 7 miles additional to what Tom travels to win the bet.

The relative speed between Karen and Tom is 60 - 45 = 15mph

Time Karen will take to cover 7 miles =  \frac{7}{15}   hours

Distance Tom travels in  \frac{7}{15}  hours =  \frac{7}{15} * 45  = 21 miles.

Total distance Tom drives before Karen wins the bet = 21 + 3 (initial distance) = 24 miles

Option D

bumpbot · Answer

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Karen places a bet with Tom that she will beat Tom in a car race by 4

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Karen places a bet with Tom that she will beat Tom in a car race by 4

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