Question

Find the value of y for which the value of 8y+3 is 7 more than the value of 6yTom and Sam can finish a plowing job in two hours if they work toghether. Tom working alone can do the job in 7 hours. How long would it take Sam to finish the same job alone?

Answer 1

19 ; 2.8 hours

Explanation:

Find the value of y for which the value of 8y+3 is 7 more than the value of 6y

8y + 3 = 7 + 6y

8y - 6y = 7 - 4

2y = 3

y = 3/2

y = 1.5

Let

Tom's rate = x

Sam's rate = y

Rate = 1 / time

Hence,

x = 1/7

Rate when they work together = 1/2

Tom's rate + Sam's rate = 1/2

1/7 + y = 1/2

y = 1/2 - 1/7

y = (7 - 2) / 14

y = 5/14

Since, rate = 1/time

Time = 1/ rate

Sam's time = 1/ rate = 1/y = reciprocal of y

Sam's time = 14/5 = 2.8 hours

2.8 hours = 2 hours (0.8 * 60) = 2 hours 48 minutes