The Car and the Bicyclist
6) Jake, in his car, and Joshua on his bike began their trip
at the same time, from the same place, but going in opposite directions.
After three hours, they were 186 miles apart. If the bike is 26 mph
slower than the car, then what were their average speeds?
In the following formula "x" will represent the rate (speed) of
the car. So "x-26" will be the speed of the bike.
3x + 3(x -26) = 186
6x -78 = 186
6x = 264
x = 44
The car, therefore, was averaging 44 mph. And when we plug
this value of x into the term for the bicyclist -- 3(x-26) --
we have 44 - 26, which equals 18 (mph). Multiplying by the 3
(hours) shows that the car covered 132 miles; and the bike, 54
-- for a total of 186 miles.