Sally drove a distance of 520 mile. Had she averaged 15mph faster, the trip would of taken 2.4 hours less. find the average speed that she drove.
To find Sally's average speed, let's break down the given information and solve step by step.
1. Let's assume Sally's average speed for the trip is "x" mph.
2. The total time it took for Sally to drive 520 miles at an average speed of "x" mph can be calculated using the formula: time = distance / speed.
Therefore, the time it took for Sally to drive 520 miles at an average speed of "x" mph is: time1 = 520 / x.
3. Now, we are given that if Sally had averaged 15 mph faster, the trip would have taken 2.4 hours less than the original time. So, the new average speed would be "x + 15" mph.
Using the same formula as before, the new time it would take for Sally to drive 520 miles at an average speed of "x + 15" mph is: time2 = 520 / (x + 15).
4. We are given that the new time is 2.4 hours less than the original time: time2 = time1 - 2.4.
Now, let's substitute the values we have and solve the equation:
520 / (x + 15) = 520 / x - 2.4.
To eliminate the denominators, we can cross-multiply:
520x = (520 - 2.4(x + 15)) * x.
Distribute on the right side:
520x = 520x - 2.4x - 36x - 2.4 * 15.
Combine like terms:
520x = 520x - 38.4x - 36.
Rearrange the equation to isolate the variable:
38.4x = 36.
Divide both sides by 38.4 to solve for x:
x = 36 / 38.4.
Calculate:
x ≈ 0.9375.
Therefore, Sally's average speed was approximately 0.9375 mph (or approximately 93.75 mph).