Stan and Hilda can mow the lawn in 25 minutes together. If Hilda works twice as fast as Stan, how long would it take Stan to mow the lawn alone?

Question

Give your answer in minutes 

Answer 1

t represents the amount of time Hilda needs

2t represents the amount of time Stan needs.

 

25/t + 25/2t = 1

2(25) + 25 = 2t      LCD, 2t

50 + 25 = 2t

75 = 2t

37.5 = t

Answer 2

Kianna, in one minute, together they complete 1/25 of the lawn. Since Hilda works twice as fast as Stan, his time is double Hilda's.

 

1/h + 1/2h = 1/25

 

The common denominator is 50h...

 

50/50h + 25/50h = 2h/50h

 

With the same denominators, thr denominators can go away...

 

50 + 25 = 2h

75 = 2h 

h = 37.5 minutes

 

So, Stan can mow in 75 minutes.

 

Let's check...

 

1/37.5 + 1/75 = 1/25

2/75 + 2/150 = 2/50

4/150 + 2/150 = 6/150

4 + 2 = 6

6 = 6

Check!