During a trip of 200 kilometres, Stella covers the first 80 kilometres at an average speed of x kilometres per hour and

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

During a trip of 200 kilometres, Stella covers the first 80 kilometres at an average speed of x kilometres per hour and

by BTGmoderatorDC » Wed Dec 16, 2020 6:00 pm

Timer

00:00

Your Answer

Global Stats

During a trip of 200 kilometres, Stella covers the first 80 kilometres at an average speed of x kilometres per hour and the remaining distance at an average speed of (x + 15) kilometres per hour. If her average speed for the entire trip is 250/3 kilometres per hour, what is the value of x?

A. 223/3
B. 75
C. 455/6
D. 80
E. A unique value cannot be determined

OA B

Source: e-GMAT

Quote

Source: Beat The GMAT — Problem Solving | Wed Dec 16, 2020 6:00 pm

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: During a trip of 200 kilometres, Stella covers the first 80 kilometres at an average speed of x kilometres per hour

by Scott@TargetTestPrep » Sat Dec 19, 2020 5:08 pm

BTGmoderatorDC wrote: ↑
Wed Dec 16, 2020 6:00 pm
During a trip of 200 kilometres, Stella covers the first 80 kilometres at an average speed of x kilometres per hour and the remaining distance at an average speed of (x + 15) kilometres per hour. If her average speed for the entire trip is 250/3 kilometres per hour, what is the value of x?

A. 223/3
B. 75
C. 455/6
D. 80
E. A unique value cannot be determined

OA B

Source: e-GMAT

Solution:

The time for the first 80 km of the trip is 80/x, and the time for the remaining 120 km of the trip is 120/(x + 15). We are given that the average speed of the entire trip is 250/3 kilometers per hour, Thus, the total time spent making the trip is 200/(250/3) = 200 x 3/250 = 4 x 3/5 = 12/5 hours. We can create the equation for the time of the trip as:
80/x + 120/(x + 15) = 12/5

Multiplying the equation by 5x(x + 15), we have:

400(x + 15) + 600x = 12x(x + 15)

400x + 6000 + 600x = 12x^2 + 180x

12x^2 - 820x - 6000 = 0

3x^2 - 205x - 1500 = 0

(3x + 20)(x - 75) = 0

x = -20/3 or x = 75

Since x can’t be negative, x = 75.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]