# Math

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Josh and Mike live 13 miles apart. Yesterday Josh started to ride his bicycle toward Mike's house. When they met, Josh had ridden for twice the length of time as Mike and at 4/5 of Mike's rate. How many miles had Mike ridden when they met?

(a) 4
(b) 5
(c) 6
(d) 7
(e) 8

• Math -

Vj = 0.8 Vm

Josh rides for time t at speed Vj
Mike rides for time t/2 at speed Vm

Vm*t/2 + Vj*t = 13
Vm*t/2 + 0.8 Vm*t = 13
1.3 Vm t = 13
Vm t = 10
The distance Mike travelled is
(1/2) Vm t = 5 miles

You cannot solve for Vm and t separately, but you don't have to to get the answer.

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