A chemical spill is leaking into a river flowing 2 3/10 miles per hour. How long will it take the chemicals to reach a town located 34 1/2 miles down stream from the spill?
To find the time it will take for the chemicals to reach the town, we need to divide the distance by the speed of the river.
The distance between the spill and the town is 34 1/2 miles.
The speed of the river is 2 3/10 miles per hour.
We can convert the mixed numbers to improper fractions for easier calculations:
The distance is 34 1/2 which is equivalent to (2 * 2) + 1/2 = 5/2 = 10/2 + 1/2 = 11/2 miles.
The speed of the river is (2 * 10) + 3/10 = 20/10 + 3/10 = 23/10 miles per hour.
To find the time it will take for the chemicals to reach the town, we will divide the distance by the speed:
Time = Distance ÷ Speed
Time = (11/2) ÷ (23/10)
To divide by a fraction, we can multiply by its reciprocal:
Time = (11/2) × (10/23)
Time = (11 × 10) / (2 × 23)
Time = 110/46
To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 2:
Time = (55/23) / (23/23)
Time = 55/23
Therefore, it will take the chemicals approximately 55/23 hours for them to reach the town.