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10 Apr 2024, 01:30
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E
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Difficulty:
35%
(medium)
Question Stats:
76% (02:36) correct
24%
(02:57)
wrong
based on 206
sessions
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Donna is a mountain biking enthusiast. One Saturday, she spent the morning biking up an uphill trail at an average speed of 20 kilometers per hour, and then returned by the same route in the afternoon at an average speed of 25 kilometers per hour. If the downhill trip in the afternoon took \(\frac{3}{4}\) of an hour less than the uphill trek in the morning, how many kilometers did Donna ride each way?
A. 50
B. 55
C. 65
D. 70
E. 75
A. 50
B. 55
C. 65
D. 70
E. 75
10 Apr 2024, 03:00
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Let the time it took Donna to cycle uphill = \(x\)
Uphill trip:
Speed = \(20 \)
Time = \(x\)
Distance = \(20x\) [Formula for distance = speed * time]
Downhill trip:
Speed = \(25\)
Time = \(x - \frac{3}{4}\)
Distance = \(25x - (25*\frac{3}{4})\)
We know that the distances of both routes are the same so we can make them equal to one another, and solve for the value of \(20x\) to find the distance of route in one way.
\(20x = 25x - (25*\frac{3}{4}) \)
\(5x = (25*\frac{3}{4})\) [multiply through by 4 to get 20x]
\(20x = 25*3\)
\(20x = 75\)
ANSWER E
Uphill trip:
Speed = \(20 \)
Time = \(x\)
Distance = \(20x\) [Formula for distance = speed * time]
Downhill trip:
Speed = \(25\)
Time = \(x - \frac{3}{4}\)
Distance = \(25x - (25*\frac{3}{4})\)
We know that the distances of both routes are the same so we can make them equal to one another, and solve for the value of \(20x\) to find the distance of route in one way.
\(20x = 25x - (25*\frac{3}{4}) \)
\(5x = (25*\frac{3}{4})\) [multiply through by 4 to get 20x]
\(20x = 25*3\)
\(20x = 75\)
ANSWER E
19 Apr 2024, 01:41
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Lets say up hill speed = S1 and time taken = t1
downhill speed = s2 and time taken = t2
Speed is inversely proportional to time ; Hence , s1/ s2 = t2/t1 = 20/25 =4/5
t1 - t2 = 3/4
solving t2= 3 hr. and t1= 15/4 hr.
Distance = 20 * 15/4 = 75 ( considering uphill speed )..
E is the answer. gmatophobia
downhill speed = s2 and time taken = t2
Speed is inversely proportional to time ; Hence , s1/ s2 = t2/t1 = 20/25 =4/5
t1 - t2 = 3/4
solving t2= 3 hr. and t1= 15/4 hr.
Distance = 20 * 15/4 = 75 ( considering uphill speed )..
E is the answer. gmatophobia
