Matt and cara take eight hours to mow the lawn. Cara alone takes four times as long as Matt. How long does Matt take alone?

Question

Matt and cara, working together, can mow a lawn in eight hours. Working alone, cara takes four times as long as Matt. How long does it take Matt to mow the lawn alone?

Answer 1

Let Matt's time alone be x hrs
let Cara's time alone be 4x hrs

let the two rates be
1/x for Matt and 1/(4x) for Cara

combined rate = 1/x + 1/(4x) = 5/(4x)

1/(5/(4x)) = 8

4x/5 = 8 hrs
4x = 40 or x = 10

Matt will take 10 hrs to mow the lawn alone

Answer 2

C = time Cara takes working alone

 

M = time Matt takes working alone

 

Given:  C = 4M

 

T = total time it takes working together = 8 hours

 

The relation to solve is

 

1/C + 1/M = 1/T

 

1/(4M) + 1/M = 1/8

 

M = 8(1/4 + 1) = 8(5/4) = 10 hours

 

C = 4M = 4(10) = 40 hours

 

It takes Matt 10 hours working alone

It takes Cara 40 hours working alone