a boat traveling at a constant speed goes 45 miles with the current, then turns around and travels for 50 miles against the current. if the speed of the current is 5 mph and the total time for the trip was 4 hours, find the speed of the boat on calm water
Let x = speed in calm water,
Then his speed with the current = x+5
And his speed against the current = x-5
Let t = time with current
then his time against the current = 4-t
Make this DRT chart:
distance | speed | time =
with current 45 | (x+5) |
against corrent 50 | (x-5)· |
The equation comes from:
Multiply through by LCD of (x+5)(x-5)
45(x-5) + 50(x+5) = 4(x+5)(x-5)
45x - 225 + 50x + 250 = 4(x²-25)
95x + 25 = 4x² - 100
Get 0 on the left side:
0 = 4x² - 95x - 125
0 = (x-25)(4x+5)
x-25=0 4x+5=0
x=25 4x=-5
x=
Ignore the negative answer.
Answer = 25 mph
Edwin