Question

A tugboat goes upstream 160 miles in 10 hours. The return trip downstream takes 5 hours. Find the speed of the tugboat without a current and the speed of the current.

Answer 1

upstream speed = speed of boat - speed of current
downstream speed = speed of boat + speed of current

it says upstream speed is 160 miles in 10 hours so that's \(\frac{160 \; \text{miles}}{10 \; \text{hours}} = 16 \; \text{mph}\)

downstream speed is 160 miles in 5 hours so 160/5 = 32 mph

now let speed of boat = b
speed of current = c

upstream speed = b - c
downstream speed = b+ c

16 = b- c
32 = b+c

you're looking for speed wihtout current so solve for b (speed of boat)