Allan drives from Boston to Washington, D.C., and then returns. On his trip to Washington, he travels 60 miles per hour. On his return trip, he travels 50 miles per hour. His trip to Boston takes and hour and a half longer than his trip to Washington. How far apart are Washington and Boston? d = rt [distance from Boston to Washington and Washington to Boston is the same]
Answers
Given : Allan drives from Boston to Washington, D.C., and then returns
On his trip to Washington, he travels 60 miles per hour.
On his return trip, he travels 50 miles per hour. His trip to Boston takes an hour and a half longer than his trip to Washington.
To Find : How far apart are Washington and Boston
Solution:
Distance = Speed x Time
Let say Time take to from Boston to Washington, D.C. = T Hrs
Speed = 60 miles per hrs
Distance = 60T
on return Time taken = T + 1 1/2 = T + 3/2 Hrs
= (2T + 3)/2 hrs
Speed =50 miles per hrs
Distance = 50T * (2T + 3)/2
Equating Distance
60T = 50T * (2T + 3)/2
=> 12 = 5(2T + 3)
=> 12 = 10T + 15
=> 2T = 15
=> T = 15/2 hrs
Distance = 60T = 60(15/2)
= 30(15)
= 450 miles
Washington and Boston are 450 miles apart
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