For the first 5 hours of a trip, a plane averaged

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

For the first 5 hours of a trip, a plane averaged

by Gmat_mission » Sun Apr 01, 2018 9:45 am

For the first 5 hours of a trip, a plane averaged 120 kilometers per hour. For the remainder of the trip, the plane traveled an average speed of 180 kilometers per hour. If the average speed for the entire trip was 170 kilometers per hour, how many hours long was the entire trip?

A. 15
B. 20
C. 25
D. 30
E. 35

[spoiler]OA=D[/spoiler].

What is the formula that I should use here? I got confused here.

Quote

Source: Beat The GMAT — Problem Solving | Sun Apr 01, 2018 9:45 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

by Vincen » Sun Apr 01, 2018 10:36 am

Gmat_mission wrote:For the first 5 hours of a trip, a plane averaged 120 kilometers per hour. For the remainder of the trip, the plane traveled an average speed of 180 kilometers per hour. If the average speed for the entire trip was 170 kilometers per hour, how many hours long was the entire trip?

A. 15
B. 20
C. 25
D. 30
E. 35

[spoiler]OA=D[/spoiler].

What is the formula that I should use here? I got confused here.

Hi.

This is how I'd solve it.

We have that $$average\ speed\ =\ \frac{\text{Total}\ \text{ Distance}}{\text{Total}\ \text{Time}}.$$ Now, "For the first 5 hours of a trip, a plane averaged 120 kilometers per hour" implies that the first part of the trip are $$d_1=v_1\cdot t_1\ =\ 120\cdot5=600\ km.$$ Now, the second one is $$d_2=v_2\cdot t_2\ =\ 180\cdot t_2.$$ Now, replacing this on the first equation we have that: $$Average\ Speed\ =\ \frac{\text{Total}\ \text{ Distance}}{\text{Total}\ \ \ \text{Time}}$$ $$170=\ \frac{d_1+d_2}{t_1+t_2}=\frac{600+d_2}{5+t_2}=\frac{600+180t_2}{5+t_2}$$ $$850+170t_2=600+180t_2$$ $$850-600=180t_2-170t_2$$ $$250=10t_2$$ $$t_2=25.$$ Now, the entire trip was $$T=t_1+t_2=5+25=30\ hours\ long.$$ Therefore, the correct answer is the option D.

I hope it helps you.

Quote

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Thu Apr 05, 2018 4:24 pm

Gmat_mission wrote:For the first 5 hours of a trip, a plane averaged 120 kilometers per hour. For the remainder of the trip, the plane traveled an average speed of 180 kilometers per hour. If the average speed for the entire trip was 170 kilometers per hour, how many hours long was the entire trip?

A. 15
B. 20
C. 25
D. 30
E. 35

We have an average rate problem for which we can use the formula:

average rate = (total distance)/(total time)

We are given that for the first 5 hours of a trip, a plane averaged 120 kilometers per hour. Thus, the distance for the first 5 hours was 120 x 5 = 600 miles.

We are also given that for the remainder of the trip, the plane traveled an average speed of 180 kilometers per hour. If we let the time for the remainder of the trip = x hours, then the distance traveled for the remainder of the trip was 180x miles.

Finally we are given that the average speed for the entire trip was 170 kilometers per hour, so we can now determine x.

170 = (600 + 180x)/(5 + x)

170(5 + x) = 600 + 180x

850 + 170x = 600 + 180x

250 = 10x

25 = x

Thus, the entire trip was 25 + 5 = 30 hours.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]