Question

Washing his dad's car alone, Enrique takes 7 hours. If his dad helps him, then it takes 2 hours. How long does it take Enrique's dad to wash the car by himself?

Answer 1

By setting up an equation using the concept of work rates, we can determine that it would take Enrique's father 2.8 hours to wash the car by himself.

Step-by-step explanation:

To solve this problem, we can set up an equation based on the concept of work rates. Enrique's work rate is 1/7 of the car per hour since he takes 7 hours to wash the car alone. If his father's work rate is 1/d where d is the number of hours his dad takes to wash the car alone, their combined work rate when working together is 1/7 + 1/d = 1/2, since they take 2 hours together.

Now, let's set up the equation from the combined work rate:

1. 1/7 + 1/d = 1/2
2. To find common denominators, we multiply each fraction by the other denominator over itself. This gives us (d + 7)/(7d) = 1/2.
3. Now, we cross-multiply to clear the fractions, getting 2(d + 7) = 7d.
4. Expanding this yields 2d + 14 = 7d.
5. Subtracting 2d from both sides gives 14 = 5d.
6. Finally, dividing both sides by 5 gives us d = 14/5 or 2.8 hours. So, Enrique's father would take 2.8 hours to wash the car alone.