A truck left City M and traveled toward City N. A second truck left

Question

A truck left City M and traveled toward City N. A second truck left City N exactly 1 hour later and traveled toward City M. The trucks passed each other after they had traveled, nonstop, a combined total of 490 miles. If the average speeds of the trucks up to the time they passed each other were 50 miles per hour (mph) and 60 mph, respectively, how far, to the nearest mile, had the first truck traveled when the trucks passed each other?

A. 223
B. 240
C. 245
D. 250
E. 300

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Official Answer

D

gmatophobia · Accepted Answer

Let's assume that the speed of the first truck ( s_1 ) = 50 mph

The speed of the second truck ( s_2 )= 60 mph

Distance covered by the first truck when the second truck begins its journey = 50 miles

Remaining distance = 490 - 50 = 440 miles

The ratio of the distance covered by the two trucks is in the ratio of their speeds

\frac{s_1}{s_2} = \frac{50}{60} = \frac{5}{6}

Hence, out of the 11 parts of the journey, the second truck covers 6 parts, and the first truck covers 5 parts.

Distance covered by the first truck =  \frac{440}{11} * 5 = 200

Total distance covered =  200 + 50 = 250

Option D

e3thekid · Answer

Truck 1 Distance: R x T --- > 50 x (t + 1) = 50t + 50
Truck 2 Distance: R x T --- > 60t

Combined Distance of both trucks = 50t +50 + 60t = 490 miles
110t + 50 = 490 
110t = 440
t = 4

Distance of truck 1: 50(4) + 50 = 200 +50 = 250 miles

Option D

nisen20 · Answer

the first truck has traveled one more hour than the second at the time two trucks pass each other

\frac{x}{50} - 1 = \frac{490 - x}{60}

x = 250

T4Star · Answer

I understood the solution. But I have a doubt in this.
The question doesn't say that the trucks are travelling at the constant speed.
Infact, question mentions the AVERAGE speed till the time trucks pass each other.

In this case, is it correct to assume that Truck 1 covered 50 miles in first hour of its journey?

Bunuel · Answer

No, assuming that the truck from City M covered 50 miles in the first hour isn't necessarily correct. The question specifies the average speed, not the constant speed. However, you can set up the equation 50t + 60(t - 1) = 490 without needing to split the distances covered in the first hour and the rest of the time. Having said that, in this particular question, assuming a constant speed would still yield the correct result.

Noida · Answer

Since in this question, we can take average speed to be equal to constant speed, here is how I did it.

In the first hour, first truck will travel 50 miles.
Total miles remaining = 490 - 50 = 440

Combined speed = 110

Time travelled = 440/110 = 4 hours.

First truck has travelled for 4 + 1 = 5 hours.

Distance travelled = 50*5 = 250 miles.

Ashwi · Answer

I assumed the distance traveled by the first truck was x. Since the first truck had traveled for 1 hour longer than the second, I set up the equation as:
x/50 - x/60 = 1

Solving this gave me x = 300. Is it because this approach works only when 2 distances are equal?

Bunuel · Answer

Yes, it's because that approach only works when the distances are equal, which they aren’t in this case. The trucks travel different distances.

djung220 · Answer

I'm a little confused. On a very basic level, how can truck 2 pass truck 1 if they have driven different amounts of miles? I understand the arithmetic, but perhaps I am missing the logical reason as to why it isn't just 245.

Bunuel · Answer

Your doubt is not clear. The trucks are traveling towards each other.

Truck 1 drove longer (by 1 hour) but at a slower speed (at 50 mph).
Truck 2 drove for less time but at a faster speed (at 60 mph).
When they meet, together they covered a total of 490 miles (so the distance between cities M and N is 490 miles).

Why should they have traveled the same distance?

djung220 · Answer

Oh yes this makes sense! For some reason I thought they were traveling in the same direction. Thank you so much!

A truck left City M and traveled toward City N. A second truck left

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A truck left City M and traveled toward City N. A second truck left

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