A car travels from one town to another at a speed of 32 mph. If it had gone 4 mph faster, it could have made the trip in 1/2 hour less time. How far apart are the towns.
distance = d
32 t = d
36 (t-.5) = d
32 t = 36 (t-.5)
32 t = 36 t - 18
4 t = 18
t = 9/2
32 t = d = 144
Ahh, I kept reading the problem wrong and thinking it said 1/2 the time rather than a 1/2 hour less time so I was setting up the problem with 36(t/2) instead of 36(t-1/2).
Thanks for your help!
To solve this problem, we can use the formula: Distance = Speed × Time.
Let's assume the distance between the towns is d miles.
If the car is traveling at a speed of 32 mph, the time it takes to travel the distance d is:
Time1 = Distance / Speed = d / 32.
If the car had traveled 4 mph faster, its speed would be 32 + 4 = 36 mph. In this case, the time it takes to travel the same distance d is:
Time2 = Distance / Speed = d / 36.
According to the problem, Time2 is 1/2 hour less than Time1. So we can write the equation:
Time1 - Time2 = 1/2.
Substituting the expressions for Time1 and Time2, we have:
(d / 32) - (d / 36) = 1/2.
Now, let's solve this equation to find the value of d, which represents the distance between the towns.
To simplify the equation, we need to find a common denominator for the fractions. The common denominator of 32 and 36 is 288.
By multiplying each term by 288, we get:
288 * (d / 32) - 288 * (d / 36) = 1/2 * 288.
Simplifying this equation:
9d - 8d = 144.
d = 144.
Therefore, the distance between the towns is 144 miles.