4 If a boat goes downstream 72 miles in 3 hours and upstream

4. If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still water respectively are ________?

a. 7 & 16 mph b. 7 & 17 mph c. 6 & 17 mph d. 6 & 18 mph e. none

Please give formula/explain

Solution

let velocity of boat be v_b in still water,velocity of river be v_r

rate =distace /time

boat goes downstream 72 miles in 3 hours

vb +vr =72/3

vb +vr=24

boat goes upstream 60 miles in 6 hours

vb-vr=60/6

vb-vr=10

solving both equations

vb+vr+vb-vr=24+10

2vb=34

vb=17 mph

vb+vr=24

17+vr=24

vr=24-17

vr=7mph

elocity of boat be v_b=17mph in still water,velocity of river be v_r=7mph