In a 40-mile trip, the first 20 miles were traveled in...

[AAPL]

In a 40-mile trip, the first 20 miles were traveled in 50mph. If the total trip average speed is 60mph, what should be the average speed in the last 20 miles?

A) 150
B) 75
C) 50
D) 45
E) 40

The OA is B.

This PS question does not apear to be difficult, but it took me too much time to solve. Does any expert has a fast way of solve it?

I think that I can solve it of the following way,
$$60=\frac{50+x}{2}$$
Then I can isolate the x and get its value, am I right? Thanks!

[GMATGuruNY]

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[GMATWisdom]

In a 40-mile trip, the first 20 miles were traveled in 50mph. If the total trip average speed is 60mph, what should be the average speed in the last 20 miles?

A) 150
B) 75
C) 50
D) 45
E) 40

The OA is B.

This PS question does not apear to be difficult, but it took me too much time to solve. Does any expert has a fast way of solve it?

I think that I can solve it of the following way,
$$60=\frac{50+x}{2}$$
Then I can isolate the x and get its value, am I right? Thanks!

You may apply short cut with the following logic
However whenever you get a doubt you should make the actual calculation.
First 20 miles he has travelled @50mph
And since average is 60mph the remaining 20 miles
he should cover at a speed which would be a liitle more than 70mph
hence option B is correct

[Scott@TargetTestPrep]

In a 40-mile trip, the first 20 miles were traveled in 50mph. If the total trip average speed is 60mph, what should be the average speed in the last 20 miles?

A) 150
B) 75
C) 50
D) 45
E) 40

We can see that the time for the first 20 miles of the trip is 20/50 = 2/5 of an hour. We can let the rate of the second 20 miles of the trip be r, so that the time for the second 20 miles is 20/r. We can create the equation:

60 = 40/(2/5 + 20/r)

60(2/5 + 20/r) = 40

24 + 1200/r = 40

1200/r = 16

1200 = 16r

75 = r

Alternate Solution:

If the average speed for the entire 40 miles is 60, but the average speed in the first 20 miles is 50, then the average speed for the last 20 miles must be greater than 60; therefore we can eliminate answer choices C, D and E.

To decide between A and B, we can try one of the answer choices. If the average speed in the last 20 miles is 150 mph, then it will take 20/150 = 2/15 hours to travel the last 20 miles. With the 20/50 = 2/5 hours spent in the first 20 miles, the total time spent is 2/5 + 2/15 = 8/15 hours and the average speed is 40/(8/15) = 15 * 5 = 75. As this is not equal to 60, we eliminate answer choice A as well and are left with B as the only possible answer.

Answer: B