Problem Solving

Hello,

Can you please assist with this question:

Sam is driving ahead of Henry at a speed of 80m/hr. If Henry is driving at a speed of 60 m/hr and is 20 miles behind Sam, how long will it take for Sam to be 40 miles ahead of Henry?

My approach was as follows:

At current time t, we have:

Rate x Time = Distance
Sam: 80 x t = 80t + 20
Henry: 60 x t = 60t

However, I am stuck at this point. Can you please assist?

Thanks,
Sri

gmattesttaker2 wrote:Hello,

Can you please assist with this question:

Sam is driving ahead of Henry at a speed of 80m/hr. If Henry is driving at a speed of 60 m/hr and is 20 miles behind Sam, how long will it take for Sam to be 40 miles ahead of Henry?

My approach was as follows:

At current time t, we have:

Rate x Time = Distance
Sam: 80 x t = 80t + 20
Henry: 60 x t = 60t

However, I am stuck at this point. Can you please assist?

Thanks,
Sri

Sam is currently 20 miles ahead of Henry.
In order to be 40 miles ahead of Henry, Sam has to cover a relative distance of another 20 miles.

Relative speed = relative distance/time
time = relative distance/relative speed
= (20)/(80-60)
= 20/20
= 1 hour

Cheers

Sam is already ahead by 20 miles, and he is also ahead in speed by 20 miles an hour. So in one hour he will be additional 20 miles ahead. Total miles that he will ahead in an hour is 40 miles.

Answer is 1 hours

gmattesttaker2 wrote:At current time t, we have:

Rate x Time = Distance
Sam: 80 x t = 80t + 20
Henry: 60 x t = 60t

However, I am stuck at this point. Can you please assist?

Thanks,
Sri

You got stuck because there are two problems with your logic.

• 1) "t" represents a span of time but in your explanation you call it "current time". If Sam travels at 80 m/hr, then 80t is the distance Sam covers over t hours.

• 2) 80t = 80t + 20 can never be right no matter what since it would mean that 20 = 0

I get that you were trying to express that Sam's distance over span of time "t" is 20 miles greater than Henry's distance. A useful techniques to perform accurate word translations is to first express the relationship is easy english: "Sam's distance is 20 more than Henry's distance" -> 80t = 20 + 60t.

This is the equation you want; from this you can solve for t=1. So after a span of 1hr, Sam's distance will be 20 more than Henry's.

-Patrick

Patrick_GMATFix wrote:

gmattesttaker2 wrote:At current time t, we have:

Rate x Time = Distance
Sam: 80 x t = 80t + 20
Henry: 60 x t = 60t

However, I am stuck at this point. Can you please assist?

Thanks,
Sri

You got stuck because there are two problems with your logic.

• 1) "t" represents a span of time but in your explanation you call it "current time". If Sam travels at 80 m/hr, then 80t is the distance Sam covers over t hours.

• 2) 80t = 80t + 20 can never be right no matter what since it would mean that 20 = 0

I get that you were trying to express that Sam's distance over span of time "t" is 20 miles greater than Henry's distance. A useful techniques to perform accurate word translations is to first express the relationship is easy english: "Sam's distance is 20 more than Henry's distance" -> 80t = 20 + 60t.

This is the equation you want; from this you can solve for t=1. So after a span of 1hr, Sam's distance will be 20 more than Henry's.

-Patrick

Hello Patrick,

Thanks a lot for the explanation.

Best Regards,
Sri

You're welcome Sri

If you found my explanation helpful, checkout this discussion on the BTG Strategy forum.

-Patrick

gmattesttaker2 wrote: Sam is driving ahead of Henry at a speed of 80m/hr. If Henry is driving at a speed of 60 m/hr and is 20 miles behind Sam, how long will it take for Sam to be 40 miles ahead of Henry?

Sam must travel 20 MORE MILES AHEAD of Henry.
Time required = (additional distance to be traveled ahead)/(rate difference).

Here, the rate difference = Sam's rate - Henry's rate = 80-60 = 20 miles per hour.
Here is the reasoning:
Every hour Sam travels 80 miles, while Henry travels 60 miles.
Result:
Sam travels 20 MORE MILES than Henry, allowing Sam to travel 20 MORE MILES AHEAD of Henry.

Thus:
Time for Henry to travel 20 more miles ahead = (additional distance to be traveled ahead)/(rate difference) = 20/20 = 1 hour.

An alternate approach is to WRITE IT OUT.
Every hour, Sam travels 80 more miles, while Henry travels 60 more miles.
Calculate the distances at each 1-hour mark until Henry is 40 miles ahead of Sam.

Start: S = 20 miles, H = 0 miles, so S is 20 miles ahead.
After 1 hour: S = 20+80 = 100 miles, H = 0+60 = 60 miles, so S is 40 miles ahead.

Thus, the time for Sam to travel 40 miles ahead of Henry = 1 hour.