Salem and Vernon ville are 168 miles apart. A car leaves Salem traveling towards Vernonville, and another car leaves Vernonville at the same time, traveling towards Salem. The car leaving Salem averages 10 miles per hour more than the other and they meet after 1 hour and 36 minutes. What are the average speeds of the car?
1 hr 36' = 1.6 hours
in that time, the cars cover 168 miles
If the slower car has speed s,
s+(s+10) = 168/1.6 = 105
2s = 95
s = 47.5
To find the average speeds of the two cars, we can start by converting the given time of 1 hour and 36 minutes to hours. Since there are 60 minutes in an hour, 36 minutes is equal to 36/60 = 0.6 hours.
Let's assume the speed of the car leaving Salem is represented by v mph.
Since the other car is traveling 10 miles per hour slower, its speed can be represented as (v - 10) mph.
We know that average speed is equal to distance divided by time. In this case, the total distance between Salem and Vernonville is 168 miles.
We can use the formula:
Distance = Average Speed × Time
For the car leaving Salem, the distance traveled in 1 hour and 36 minutes can be calculated as:
Distance = v × (1 + 0.6) = v × 1.6
For the other car, the distance traveled in 1 hour and 36 minutes can be calculated as:
Distance = (v - 10) × (1 + 0.6) = (v - 10) × 1.6
Since they meet after 1 hour and 36 minutes, their total distance traveled should equal the total distance between Salem and Vernonville:
v × 1.6 + (v - 10) × 1.6 = 168
Now we can solve this equation to find the value of v:
1.6v + 1.6(v - 10) = 168
1.6v + 1.6v - 16 = 168
3.2v - 16 = 168
3.2v = 184
v = 184 / 3.2
v ≈ 57.5
So, the average speed of the car leaving Salem is approximately 57.5 mph, and the average speed of the other car is approximately (57.5 - 10) = 47.5 mph.