Mike can finish a job alone in 40 days. If Ike works on the job for 10 days and Mike joins in on the eleventh day, they can complete the job by working together for another 20 days. How many days would it take for Ike to finish the job if he worked alone?

Question

Can someone help me understand this one?

1493 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-31T01:59:46

$\frac{80}{3} or 26 \frac{2}{3}$ $80/3 or 26 2/3$

Mike can finish a job alone is $40$ $40$ days. So in a day, Mike finishes $\frac{1}{40}$ $1/40$ of a job.

Let the number of days Ike can finish a job be $x$ $x$ ,

$10 \cdot \frac{1}{x} + 10 \cdot (\frac{1}{x} + \frac{1}{40}) = 1$ $10*1/x+10*(1/x+1/40)=1$

Expand,

$\frac{10}{x} + \frac{10}{x} + \frac{10}{40} = 1$ $10/x+10/x+10/40=1$

Simplify,

$\frac{20}{x} = \frac{3}{4}$ $20/x=3/4$

Cross multiply,

$3 x = 80$ $3x=80$

Solve,

$x = \frac{80}{3}$ $x=80/3$

Ike can finish the job in $26 \frac{2}{3}$ $26 2/3$ days.