jzw wrote:The distance from the south entrance to the north entrance of a certain straight bicycling trail is 88 miles. At 11:00 AM, Zelda starts biking from the north entrance towards the south entrance of the trail. At 1:00 PM, Frank starts biking from the south entrance towards the north entrance of the trail. If Zelda is biking at a constant rate of 8 miles per hour and Frank is biking at a constant rate of 10 miles per hour, how many miles will Zelda have biked when she passes Frank on the trail?
(a) 48
(b) 46
(c) 44
(d) 42
(e) 41
From 11am to 1pm, the distance traveled by Zelda = r*t = 8*2 = 16 miles.
Remaining distance between Zelda and Frank = 88-16 = 72 miles.
When elements travel TOWARD EACH OTHER, they WORK TOGETHER to cover the distance between them, so we ADD THEIR RATES.
Time for Zelda and Frank to travel 72 miles = d/r = 72/(8+10) = 4 hours.
Distance traveled by Zelda in 4 hours = r*t = 8*4 = 32 miles.
Total distance traveled by Zelda = 16+32 = 48 miles.
The correct answer is
A.
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