SOLUTION: A motorcyclist and a cyclist travel from A to B. They leave simultaneously from A at 12 noon. The motorcyclist arrives at B after 1 ½ hours, and the cyclist arrives 30 minutes late

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Question 1011611: A motorcyclist and a cyclist travel from A to B. They leave simultaneously from A at 12 noon. The motorcyclist arrives at B after 1 ½ hours, and the cyclist arrives 30 minutes later. At what time was the cyclist twice as far from B as the motorcyclist was?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
                    rate          time         distance

morotcyclist       d/(1&1/2)      1&1/2        d

cyclist            d/2            2            d


Compare their rates.
%282%2F3%29d Motorcycle
%281%2F2%29d Cyclist

At what time t was .....
                 rate           time        distance   Distance from B
mototcycl        (2/3)d          t          (2/3)dt    d-(2/3)dt
cycl             (1/2)d          t          (1/2)dt    d-((1/2)dt

When was cylcist twice as far from B as was motorcyclist?
d-%281%2F2%29dt=2%28d-%282%2F3%29dt%29

That equation uses two unknown variables, d and t; and one of them will be found as factor on both members.

d%281-t%2F2%29=2d%281-2t%2F3%29
1-t%2F2=2%281-2t%2F3%29
LCD is 2%2A3.
6-3t=2%286-4t%29

6-3t=12-8t
6-12=-8t%2B3t
12-6=8t-3t
6=5t
highlight%28t=6%2F5%29
highlight%281%261%2F5%29 hours
1 hour 12 minutes