Question

Josh and mike live 13Km apart. Josh started to ride his bicycle towards mikes house.A little later Mike started to ride his bicycle towards Josh's house. when they met, Josh had ridden for twice the length of time as Mike and at four-fifths of Mike's rate. How many kilometers had mike ridden when they met?

Answer 1

Remark
The general formula for this is distance = rate * time or more briefly d = r * t

Step One
Fill out as much as possible for each bike rider.

Mike
d = d
r = r
t = t

Josh
d1 = 13 - d
r1 = 4/5 * r
t1 = 2 * t

Equation
r1 * t1 + r * t = 13

substitute and solve
4/5 r * 2t + r*t = 13
(8/5) r * t + r*t = 13 Take out the common factor of rt
rt(8/5 + 1 ) = 13 change 1 to 5/5 and add.
rt(8/5 + 5/5) = 13 Divide by 13/5
rt(13/5) = 13
rt = 13/(13/5) =
`((13)/(1))/((13)/(5) )` Invert the bottom fraction and multiply.
rt =
`(13)/(1) * (5)/(13) = 5` Note that the 13s cancel.

Answer
Mike traveled 5 km.
rt = 5 <<<< Answer

Notice that you only need rt together. You don't need to know exactly what either one of them is.

Every so often someone comes up with a unique question using d=r*t. You are the lucky person today. Thanks for posting.