Just wanted to check to see if these are correct. Thank you,
Please check
if a greyhound bus travels 7mph slower than the express bus. the express bus travels 45 miles in the time it takes the greyhound bus to travel 38 miles. find the speed of each bus
greyhound 38/x-7 express 45/x
38/x-7=45/x
38x=45x-315
-7x=-315
x=45
45-7=
38mph for greyhound
45mph for express
Correct :)
The answer is correct!
However, please be careful with parenthese:
38/x-7 ≡ (38/x) - 7
because multiplications and divisions take precedence over additions and subtractions.
If you want 38/(x-7), you need the parentheses.
A general rule is to insert parentheses around the numerator and denominator.
To solve this problem, we can set up equations based on the given information.
Let's assume the speed of the express bus is x mph. According to the problem, the greyhound bus travels 7 mph slower than the express bus, so its speed would be (x - 7) mph.
Next, we need to find the time it takes for each bus to travel their respective distances. We can use the formula:
time = distance / speed
For the express bus:
time = 45 miles / x mph
For the greyhound bus:
time = 38 miles / (x - 7) mph
Since we are given that the time for the greyhound bus is the same as the time for the express bus, we can set up the equation:
38 / (x - 7) = 45 / x
Now, we can solve this equation for x.
To do that, we can cross-multiply:
38x = 45(x - 7)
Expanding the right side:
38x = 45x - 315
Moving the variables to one side:
7x = 315
Dividing both sides by 7:
x = 45
Now, we have found that the speed of the express bus is 45 mph.
To find the speed of the greyhound bus, we substitute this value back into the expression (x - 7):
Greyhound speed = 45 - 7 = 38 mph
Therefore, the speed of the greyhound bus is 38 mph, and the speed of the express bus is 45 mph.