It takes Sarah, traveling at 24mph
, 10
minutes longer to go a certain distance than it takes Ricky traveling at 32mph
. Find the distance traveled.
Let's start by using the formula:
distance = rate x time
Let d be the distance traveled. Then we have:
d = 24(t + 10) (for Sarah)
d = 32t (for Ricky)
where t is the time it takes for Ricky to travel the distance.
We want to find the value of d. We can solve for t in the second equation:
t = d/32
Now we can substitute this expression for t in the first equation:
d = 24(t + 10)
d = 24(d/32 + 10)
d = 18d/8 + 240 (dividing both sides by 4)
8d = 144d/8 + 960
7d = 960
d = 137.14 (rounded to two decimal places)
Therefore, the distance traveled is approximately 137.14 miles.
To find the distance traveled, we need to use the formula:
Distance = Speed × Time
Let's assume the distance traveled is represented by "d."
We are given that Sarah's speed is 24 mph and it takes her 10 minutes (or 10/60 = 1/6 hour) longer than Ricky to travel the same distance.
Let's denote the time taken by Ricky as "t" (in hours).
We know that Ricky's speed is 32 mph. So we can set up the equation:
d = 32t
Since Sarah takes 10 minutes longer than Ricky, her time can be expressed as (t + 1/6) hours.
So, we can set up the equation for Sarah:
d = 24(t + 1/6)
Now we can solve these two equations simultaneously to find the value of "d."
1) d = 32t
2) d = 24(t + 1/6)
We can substitute the value of d in equation 2) with the value of d from equation 1):
32t = 24(t + 1/6)
Simplifying the equation:
32t = 24t + 4
Moving the terms involving "t" to one side and the constant term to the other side:
32t - 24t = 4
8t = 4
Dividing both sides by 8:
t = 4/8
Simplifying further:
t = 1/2 hour
Now, we can substitute the value of t back into equation 1) to find the distance traveled:
d = 32t
d = 32 * (1/2)
d = 16
Therefore, the distance traveled is 16 miles.