Question

A boat traveled 210 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?

Answer 1

Try this solution:

Answer: 6 & 4.5 (m-per-h)

Explanation:

- The basic formula used in this task is S=V*t, where S - distance, V - speed, t - time.

- the downstream speed is: V+Vc, where V - the speed of the boat in still water, Vc - the speed of the current.

- the upstream speed is: V-Vc.

- according to the described above the distance for downstream is S1=(V+Vc)*t1, where t1=10; the distance for upstream is S2=(V-Vc)*t2, where t2=70.

- for whole travel down- and upstream: S=S1+S2.

- Using these it is possible to make up the system of the equations:

`\left \{ {{(70(V-V_c)=10(V+V_c)} \atop {70(V-V_c)+10(V+V_c)=210}} \right.`

V - the speed of the boat in still water - 6 miles per hour, Vc - the speed of the current - 4.5 miles per hour. All the details for the system of the equations are in the attachment.