Zeta always runs around the track at a rate of 30 laps per 75 minutes, and Ray always runs at the rate of 20 laps per 40 minutes. If they start at the sme time, how many minuts will it take them to run a combined distance of 99 laps?

Question

Zeta always runs around the track at a rate of 30 laps per 75 minutes, and Ray always runs at the rate of 20 laps per 40 minutes.  If they start at the sme time, how  many minuts will it take them to run a combined distance of 99 laps?

unklerhaukus · Answer

$$ \zeta = \frac{30laps}{75mins}=40 \frac{laps}{hour}$$
$$\rho= \frac{20laps}{40mins}=30\frac{laps}{hour}$$

so after 1 hour zeta and ray have a combined total of 70 laps
after 1 minute they have a combined total of 7 laps

after 1 hour and 4 minutes the have a total of 70 +4x7 =98 laps
in the 5th minute after the first hour , zeta and ray will have completed 99 laps

hero · Answer

Hint: 

$$\frac{30}{75} + \frac{20}{40} = \frac{99}{x}$$

hero · Answer

I get x = 1 hour , 50 minutes

Would anyone like to know the full steps?

unklerhaukus · Answer

yes