Answer for this question

Question

a motorboat maintained a constant speed of 17 miles per hour relative to the water in going 42 miles upstream and then returning the total time for the trip was 8.5 hours use this information to find the speed of the current

Answer 1

8.5 hours to go 2(42) = 84 miles

boat speed relative to water = 17 mph

current speed = 11 mph

(b+c)x = 42 = (b-c)(8.5-x)

where b=boat's speed = 17, c=current speed, x = time downstream, 8.5-x = time upstream

(17+c)x =42 downstream

(17-c)(8.5-x) =42 upstream

x=1.5 hour downstream, 7 hours upstream

c= 11 mph = current speed

(17+11)(1.5)=42

(17-11)(7) = 42

c= 42/x -17

c = 17-42/(8.5-x)

42/x -17 = 17 -42/(8.5-x)

multiply by x(8.5-x)

use quadratic formula

x = [289+/- sqr(289^2- 4(34)(357)]/68= 1.5,7

c=42/1.5-17 = 11 mph = current speed