Speed problem

Question

Hi all
can any one explain this to me please.

It takes Tanya 50 minutes to drive to the country club. If the average speed of the entire round trip to the club is 87.5% of the average speed on the way to the club, how many minutes approximately will it take Tanya to drive home from the country club?
42 minutes.
48 minutes.
52 minutes.
54 minutes.
66 minutes.

ian7777 · Answer

well, my answer is approx. 64.2 minutes, so I think I'm going with E, 66 minutes.

We have a rate problem with 2 fractions in it: 5/6 is the time in hours of the first leg (50 minutes), and 7/8 is the percent overall of the one way speed. So I picked a number that worked with 6 and 8 as the original speed: 48.

So at 48 mph for 50 min (5/6 hours) = 40 miles.
7/8 of 48 = overall average speed = 42 mph.

Total overall distance = 40x2 = 80

So total overall time = D/r = 80/42 = 40/21 hr = approx = 114.2 minutes.

Time of second leg = total time minus first leg = 114.2 - 50 = 64.2 minutes.

Sorry for the long explanation, but this one had a lot of steps. Hope it was clear.

venksune · Answer

Ian,
I also got it as 64.28. I waswondering if I am making any mistakes..you kind of established that I am in the right track. 

I again feel that this is out of scope from GMAT point of view - what's your take.

ian7777 · Answer

Hi venksune, 

no, i think this is right in line with the gmat. I think this could absolutely be on the test. In fact, this is the kind of problem I hope is on the test. All the numbers work out very well, and with all the fractions, everything (potentially) can cancel out (even though there's a decimal, it's not too bad).

where's it from, saurya_s?

saurya_s · Answer

Thank you all, You guys are right. Is it outside GMAT standard? I would love if they don't aks questions like this.

al1234 · Answer

Hello, 

 Here is a bit different approach:
Let' s take the speed of Tanya as 
v(A,B) = D / t1 , where A represent home, B the club; D is the distance she took and t1 is the time she walked from home to the club ( 50 min )
Let v(B,A) represent the speed from the club to home.
 Based on the instruction :
(v(A,B) + v(B,A) ) / 2 = 0.875 * v(A,B)
From here we get: 

v(B,A) = .75 * v(A,B)

Since v(B,A) = D / t2 we need to solve our equation for t2.

v(A,B) / v(B,A ) = t2 / t1

t2 = 50 / .75 = 50 / ( 3/4 ) = 200 / 3 = 66.6

saurya_s · Answer

Hi al
Are you right in taking average speed as (v(A,B) + v(B,A) ) / 2? shouldn't it be total distance/total time rather than this?
S

bigtooth81 · Answer

We have the equation:

 D/50 =   * 100/87.5
 x = 2500/87.5 = 66.6..

ian7777 · Answer

Remember that we can never take the average of two rates. It doesn't work that way. 

If, for example, a person drives 120 miles each way, the first time going 30 miles per hour, and the second time going 60 miles per hour, we cannot say their average speed is 45 miles per hour. We must recognize that it takes 4 hours going one way and 2 hours the other way, meaning a total of 240 miles in 6 hours. So the average rate is 40 miles per hour.

In this case, it seems that doing the problem both ways comes up with an answer of roughly 65 minutes. But that's just luck. On a different problem, making this mistake usually means getting the problem wrong.

saurya_s · Answer

Ian, you have confirmed what I thought, thanks
S

al1234 · Answer

Hi, Yep, Ian you are right, :beat

The average is indeed what you explained : 2D/(t2+50) So after all t2 = 64.28

venksune · Answer

Arithmetic mean is not right when calculating average of speeds. Typically it has to be Harmonic Mean 

Avg Speed = ((Speed1 x time1) + (Speed 2 x time2))/(time1 + time2). Or Simply put (D1+D2)/(t1+t2). No marks for guessing D1 and D2 as distances.

krish · Answer

E is my choice. Managed to get 64.#@@#@

Speed problem

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