Question

A boat traveled downstream a distance of 36 mi and then came right back. If the speed of the current was 12 mph and the total trip took 4 hourscomma nbsp, find the average speed of the boat relative to the water.

The boat had an average speed of ____________ mph relative to the water.

​(Simplify your​ answer.)

Answer 1

Given, The distance travelled by boat(d_d)= 36 mi down stream

The distance travelled by boat(d_u)= 36 mi upstream

Total distance(d) = d_d+d_u= 36+36= 72 mi

Speed of stream (S_s)= 12 mph

let speed of boat be S_b

in upstream, boat and water travel in opposite direction, implies the relative speed is

Speed of boat in upstream= s_bu= S_b-12

Speed of boat in downstream= s_bd= S_b​+12

Total travel time(t) = 4 hours= t_up+t_down

We know that, timexspeed = distance

t_up= d_u/(S_b-12)

tdown= d_d/(S_b+12)

t = t_up+t_{down = 4}

4 = d_u/(S_b-12) + d_d/(S_b+12)

4 = 36_/(S_b-12) + 36_/(S_b+12)

on simplification, equation becomes S_b²-18S_b-144 = 0, the roots are (S_b-24)(S_b+6)

So, Speed of boat S_b= 24 mph is the answer