Question

bob and ross are both work as painters. bob can paint 2 rooms in 130 minutes, and ross can paint 3 rooms in 170 minutes. at this rate, if bob and ross each work 10 - hour shifts, many days will it take bob and ross to paint a 200 - room apartment complex? days =

Explanation:

Step1: Calculate Bob's rate

Bob can paint 2 rooms in 130 minutes. So his rate $r_{Bob}=\frac{2}{130}=\frac{1}{65}$ rooms per minute.

Step2: Calculate Ross's rate

Ross can paint 3 rooms in 170 minutes. So his rate $r_{Ross}=\frac{3}{170}$ rooms per minute.

Step3: Calculate combined rate

The combined rate $r = r_{Bob}+r_{Ross}=\frac{1}{65}+\frac{3}{170}$.
Find a common - denominator, which is $2210$. Then $\frac{1}{65}+\frac{3}{170}=\frac{1\times34}{65\times34}+\frac{3\times13}{170\times13}=\frac{34 + 39}{2210}=\frac{73}{2210}$ rooms per minute.

Step4: Calculate total minutes

There are 200 rooms. Using the formula $t=\frac{W}{r}$ (where $W$ is work and $r$ is rate), $t=\frac{200}{\frac{73}{2210}}=200\times\frac{2210}{73}=\frac{442000}{73}$ minutes.

Step5: Calculate number of 10 - hour shifts

Each shift is 10 hours or $10\times60 = 600$ minutes. The number of shifts $n=\frac{\frac{442000}{73}}{600}=\frac{442000}{73\times600}=\frac{442000}{43800}=\frac{2210}{219}\approx10.091$ shifts.

Step6: Calculate number of days

Since they work 1 shift per day, the number of days is $\lceil\frac{2210}{219}
ceil = 11$ days.

Answer:

11