Working together, 2 conveyors can fill a certain bin in 6hrs.If 1 conveyor works 1.6 times faster than the....

Working together, 2 conveyors can fill a certain bin in 6hrs. If 1 conveyor works 1.6 times faster than the other, how long(hrs) would it take each one working alone to fill the bin?the fast one first.

Let f = fast one's speed in bins/hour and s = slow one's speed in bins/hour.
6(f + s) = 1 bin
f = 1.6s
solve the system of equations:
6(1.6s + s) = 1
6(2.6s) = 1
15.6s = 1
s = 1/15.6 bins/hour = 15.6 hours/bin
f = 1.6(1/15.6) = 0.102 bins/hour = 9.75 hours/bin

Let 1 conveyor take 10x hours

Other conveyor will take 16x hours

1/10x + 1/16x = 1/6

MULTIPLY BY 240x

24 + 15 = 40x

x = 39/40

Fast one = 10x = 390/40 = 9.75 hours

Slow one = 16x = 15.6 hours ANSWER