If Bob mows a lawn in 45 minutes and Tom and Bob together mow the lawn in 35 minutes how long does it take tom

Question

If Bob mows a lawn in 45 minutes and Tom and Bob together mow the lawn in 35 minutes how long does it take tom

Answer 1

Let t_b= the time it takes Bob to mow the lawn which is 45 minutes

Let t_t= the time it takes Tom to mow the lawn which is the unknown variable

Let t_bt = the time it takes them working together.

 

1/45+1/t_t=1/25

-1/45        -1/45

 

1/t_b=18/450-10/450 = 8/450

 

Hence, t_b=450/8 = 56 2/8 = 56 1/4 Hours

 

Therefore, it would take Tom 56 1/4 Hours for Tom to mow the lawn working alone.