Josh and Mike live 13 miles apart. Yesterday, Josh started to ride his bicycle toward Mike's house. A little later Mike started to ride his bicycle toward 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 miles had Mike ridden when they met?

Question

sepeario · Answer

haha http://www.artofproblemsolving.com/wiki/index.php/2005_AMC_10A_Problems/Problem_7

dan815 · Answer

twice the time, at 4/5th of mike's rate

anonymous · Answer

is it 5 miles?

anonymous · Answer

$$2*\frac{ 4 }{ 5 }d = \frac{ 8 }{ 5 }$$
$$\frac{ 8 }{ 5 }d + d = \frac{ 13 }{ 5 }$$
$$\frac{ 13 }{ 5 }d = 13$$
d = 5

dan815 · Answer

since he travelled twice the time at 4/5th of his rate you have this ratio of distance between them

8/5 : 1

8/5 d : d

8/5 d + d = 13
d=5