# A boat travels210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?

Oct 3, 2015

I considered that the trip downstream is $210 \text{miles}$ AND the trip upstream is $210 \text{miles}$ as well but if it is different simply substitute into the explanation.

#### Explanation:

Call the speed of the boat ${v}_{b}$ and the speed of the current ${v}_{c}$ so you have:
downstream: ${v}_{b} + {v}_{c} = \frac{210}{10} = 21$
upstram: ${v}_{b} - {v}_{c} = \frac{210}{70} = 3$
where I used the fact that speed=distance/time;
from the second equation we have:
${v}_{b} = 3 + {v}_{c}$ substitute into the first equation:
$3 + {v}_{c} + {v}_{c} = 21$
$2 {v}_{c} = 18$
${v}_{c} = \frac{18}{2} = 9 \frac{\text{miles}}{h r}$
and in ${v}_{b} = 3 + {v}_{c}$ gives you:
${v}_{b} = 3 + 9 = 12 \frac{\text{miles}}{h r}$