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John has two pumps to inflate his raft. One pump can fill the raft 1.25 times as fast as the second pump. When John uses both pumps, the raft is inflated in 5 hours. How long would it take John to inflate the raft if he only used the slower pump?

Respuesta :

samuelonum1

Answer:

1.6hours

Step-by-step explanation:

let let the slower pump take x hours

then the faster pump will take 1.25x hours to pump the raft

The combined work rate is 5 hours

The expression for the combined work rate is

1/x+1/1.25x= 1/5

solve for x we have

1.25+x/1.25x= 1/5

cross multiply we have

5(1.25+x)= 1.25x

6.25+5x=1.25x

collect like terms

6.25+5x-1.25x=0

6.25+3.75x=0

3.75x=-6.25

divide both sides by 3.75

x=-6.25/3.75

x=-1.6 hours

x= 1.6hours