20 minutes because twice as fast of 20 is 40
20*2=40
Gab and Van can mow the lawn in 40 minutes if they work together. If Gab works twice as fast as Van, how long does it take Gab to mow the lawn alone ?
2 answers
time taken by Gab ---- x minutes
time taken by Van ---- 2x minutes
Gab's rate = 1/x
Van's rate = 1/2x
combined rate = 1/x + 1/(2x)
= 3/(2x)
so 1/(3/2x) = 40
2x/3 = 40
2x = 120
x = 60
Gab's time alone is 60 minutes, Van's time alone is 120 minutes
check:
combined time = 1/60 + 1/120
= 3/120 = 1/40
time at combined rate = 1/(1/40) = 40
time taken by Van ---- 2x minutes
Gab's rate = 1/x
Van's rate = 1/2x
combined rate = 1/x + 1/(2x)
= 3/(2x)
so 1/(3/2x) = 40
2x/3 = 40
2x = 120
x = 60
Gab's time alone is 60 minutes, Van's time alone is 120 minutes
check:
combined time = 1/60 + 1/120
= 3/120 = 1/40
time at combined rate = 1/(1/40) = 40