Question

1. Working alone, Jamie can mow her lawn in 75 minutes. If Bob helps her, then the two
can mow the lawn in 30 minutes. How long does it take Bob to mow the lawn alone?​

Answer 1

Given :  Working alone, Jamie can mow her lawn in 75 minutes. If Bob helps her, then the two  can mow the lawn in 30 minutes.

To Find : How long does it take Bob to mow the lawn alone?​

Solution:

Jamie can mow her lawn in 75 minutes.

=> Jamie can mow her lawn 1 minute = 1/75

Bob can mow her lawn in B minutes.

=> BoB can mow her lawn 1 minute = 1/B

Together both can mow in 1 minute =  1/75 + 1/B

= (B + 75)/75B

Together both can mow in 1 minute = 1/30

Equate both

=> (B + 75)/75B = 1/30

=> B + 75 = 75B/30

=> B + 75  = 5B/2

=> 2B + 150 = 5B

=> 3B = 150

=> B = 50

it take  Bob 50 minutes to mow the lawn alone

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Answer 2

Given :

• Jamie can mow her lawn in 75 minutes
• If Bob helps her, then the two can mow the lawn in 30 minutes

To Find :

• How long does it take Bob to mow the lawn alone ?

Solution :

We have,

• Jamie's working speed = 1/75 job/min
• Bob's speed = 1/x job/min

A.T.Q :

➠ 1/75 + 1/x = 1/30

➠ 1/x = 1/30 - 1/75

➠ 1/x = (5 - 2)/150

➠ 1/x = 3/150

➠ 150 = 3x

➠ - 3x = - 150

➠ x = (- 150)/(- 3)

➠ x = 50

∴ It take Bob 50 minutes to mow the lawn alone.

Verification :

We have,

• 1/75 + 1/x = 1/30

Substituting the value of x we get,

➠ 1/75 + 1/50 = 1/30

➠(2 + 3)/150 = 1/30

➠5/150 = 1/30

➠ 1/30 = 1/30

HENCE VERIFIED