You commute 56 miles one way to work. The trip to work takes 10 minutes longer than the trip home. Your average speed on the trip home is 8 miles per hour faster. What is your average speed on the trip home?
I don't understand why it has to be converted to 10/60. Cause it is already in miles per hour. You said that it has to be converted because it is in kilometers per hour but the question definitely says miles per hour.
i don't need help anymore. I called my friend who clearly explained it to me. And I figured it out with ease after talking to him.
I NEED HELP
Apologies for the confusion, let's clarify the conversion calculation.
To find your average speed on the trip home, we need to know the time it takes for both the trip to work and the trip home. The question states that the distance you commute one way is 56 miles, and the trip to work takes 10 minutes longer than the trip home.
Let's define some variables:
- Let T1 be the time for the trip to work (in hours).
- Let T2 be the time for the trip home (in hours).
- Let V1 be your average speed on the trip to work (in miles per hour).
- Let V2 be your average speed on the trip home (in miles per hour).
From the given information, we know that T1 = T2 + 10/60 (converted to hours). This 10/60 represents the additional 10 minutes on the trip to work.
Also, it is stated that your average speed on the trip home (V2) is 8 mph faster than your average speed on the trip to work (V1).
Now, let's set up a equation:
T1 = 56 / V1 (since speed = distance / time)
T2 = 56 / V2
We can substitute T1 and T2 using the relationship given above:
T1 = T2 + 10/60
56 / V1 = 56 / V2 + 10/60
Next, we can use the fact that V2 is 8 mph faster than V1:
V1 + 8 = V2
Now we have a system of equations to solve for V2:
56 / V1 = 56 / (V1 + 8) + 10/60
To solve this equation, we can cross multiply:
56 * (V1 + 8) = 56 * V1 + (10/60) * V1
Distributing and simplifying:
56V1 + 448 = 56V1 + (10/6)V1
Canceling out the 56V1 on both sides:
448 = (10/6)V1
To solve for V1, we can multiply both sides by 6/10:
448 * (6/10) = V1
V1 = 268.8 mph
Since we know V2 is 8 mph faster than V1:
V2 = V1 + 8
V2 = 268.8 + 8
V2 = 276.8 mph
Therefore, your average speed on the trip home is approximately 276.8 miles per hour.