Question

Lingjin drove from los angeles to ventura during rush hour at an average speed of 4545 miles per hour, and then drove back the same way at an average speed of 3030 miles per hour. if the round trip took 3 hour and 15 minutes, how many miles is lingjin's one-way trip from ventura to los angeles?

Answer 1

45mph times x hours one way
30mph times y hours back
x+y=3 hours 15 minutes

45mph(x)=z miles
30mph(y)=smiles
so
$45x = 30y \\ x = \frac{30}{45} y \\ x = \frac{2}{3} y$
and substituting we know 15 minutes is 1/4 an hour so we have
$x + y = 3.25 \\ \frac{2}{3} y + y = 3.25 \\ \frac{5}{3} y = \frac{13}{4} \\ y = \frac{13}{4} ( \frac{3}{5} ) \\ y = \frac{39}{20}$
so 1.95 is how long they were going 30mph
1.95hours time 30mph is 58.5 miles.
so that is the distance. check by putting in y and solving for x. multiply x by 45 and you should get the same distance