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

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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!

Noise1st · Answer

That explanation makes sense!

SS990 · Answer

The total distance is 490miles
1st truck starts 1 hr early, so it would have covered 50miles in 1hr (s=50m/h), when truck 2 starts. 
Distance left to cover = 490-50=440 miles
Relative speeed of 2 trucks = 60+50=110mph (since they move in opposite directions)
Total time = 440/110 = 4hrs
Truck 1 started an hour early so its been travelling for 5 hrs so distance is 50*5=250 
or we can fo 50*4 + 50 covered at the start by truck 1= 250miles

bishal128 · Answer

Combined Distance/Relative Speed =t, here when they met they would have travelled for same amount of time, thus, 490/(50+60)=49/11, for first train travelling at 50 mph, the total distance would be 50*49/11~50*50/10=250

Can this be used Bunuel?

Can this be used  Bunuel ?

Bunuel · Answer

Not quite. That setup assumes both trucks traveled for the same amount of time, but the second truck left 1 hour later.

You can use relative speed only after the second truck starts. In the first hour, the first truck travels 50 miles, so the remaining combined distance is 490 - 50 = 440 miles.

Then the trucks approach each other at 50 + 60 = 110 mph, so they meet 440/110 = 4 hours later.

Thus, the first truck traveled for 5 hours total, or 50 * 5 = 250 miles.

egmat · Answer

Hi bishal128,

Your relative-speed instinct is good, but there's one hidden assumption breaking it: dividing combined distance by combined speed only gives a single shared travel time  if both trucks start at the same moment . Here they don't - the first truck has a  1 -hour head start.

Where the shortcut slips:490/(50+60)  assumes both trucks were on the road for the same number of hours. But the first truck drove for  1  hour  before  the second even left. So there is no single common time you can plug in straight away.

Let me also flag the arithmetic, because it's hiding the trap.  490/110 = 49/11 ≈ 4.45  hours, and  50 × 4.45 ≈ 223  - that's answer  A , the classic trap, not  250 . Your approximation  50 × 49/11 ≈ 50 × 50/10 = 250  rounded  49/11  up to  5 , which overshoots. So the shortcut as written actually lands on  223 , not  250 .

The fix - peel off the head start first: 
- In its solo first hour, truck 1 covers  50 miles .
- Distance left to close together:  490 − 50 = 440 .
-  Now  both are moving, so combined speed applies:  440/110 = 4  hours.
- Truck 1's total time:  4 + 1 = 5  hours -  50 × 5 = 250 miles .

That's exactly the route Noida and SS990 used in the thread - relative speed  does  work, you just apply it only to the stretch where both trucks are actually driving.

One quick check to lock the idea in:  suppose truck 1 had a  2 -hour head start instead. It would cover  100  miles alone, leaving  390  to close at  110  mph. The combined-speed formula only ever applies to the distance covered  while both are moving  - never to the head-start miles.

Answer: D

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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