Answer:
speed of the boat: 30 mi/h, speed of the current: 10 mi/h
Explanation:
- During the trip downstream, the boat traveled 280 miles with a speed of (v+c), where v is the speed of the boat and c is the speed of the current. Since the time taken is 7 h, we can write the following equation:
\(7(v+c) =280\)
which is the equivalent of \(time \cdot speed = distance\)
- During the trip upstream, the boat traveled 280 miles with a speed of (v-c), where v is the speed of the boat and c is the speed of the current. Since the time taken is 14 h, we can write the following equation:
\(14(v-c) =280\)
So we have two equations that we can solve simultaneously to find v and c:
\(7(v+c)=280\\14(v-c)=280\)
Solving:
\(7v+7c=280\\14v-14c=280\)
Multiplying first equation by 2:
\(14v+14c=560\\14v-14c=280\)
By adding 2nd equation to 1st one, we get
\(28v=840\\14v-14c=280\)
From 1st equation we get
\(v=30\)
Substituting into second one we get
\(14(30)-14c=280\\420-14c=280\\-14c=-140\\c=10\)
So, we have:
- speed of the boat in stil water: 30 mi/h
- speed of the current: 10 mi/h
