A bus traveled on a straight road for 3 h at an average speed that was 15 mph faster than its average speed on a winding road. The time spent on the winding road was 4 h. Find the average speed on the winding road if the total trip was 220 mi
A bus traveled on a straight road for 3 h at an average speed that was 16 mph faster than its average speed on a winding road. The time spent on the winding road was 3 h. Find the average speed on the winding road if the total trip was 210 mi.
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mph
To find the average speed on the winding road, we can first determine the distance traveled on the winding road by subtracting the distance traveled on the straight road from the total distance.
Let's assume the average speed on the winding road was "x" mph.
The distance traveled on the straight road can be calculated by multiplying the speed on the straight road (which is x + 15 mph) by the time spent on the straight road (which is 3 hours):
Distance on the straight road = (x + 15) mph * 3 hours = 3x + 45 miles
Now, we can calculate the distance on the winding road by subtracting the distance on the straight road from the total distance of 220 miles:
Distance on the winding road = Total distance - Distance on the straight road
Distance on the winding road = 220 miles - (3x + 45 miles)
Distance on the winding road = 220 miles - 3x - 45 miles
Distance on the winding road = 175 miles - 3x
We know that the time spent on the winding road is 4 hours, so we can use the formula for average speed:
Average speed = Total distance / Total time
Average speed on the winding road = (175 miles - 3x) / 4 hours
Since the average speed on the winding road is what we want to find, we can now set up the equation:
Average speed on the winding road = (175 miles - 3x) / 4 hours = x mph
Now, let's solve for x:
175 miles - 3x = 4x
175 miles = 7x
x = 25 miles per hour
Therefore, the average speed on the winding road is 25 mph.