A chemical spill is leaking into a river flowing 2 3/10 mile per hour . How long will it take the chemicals to reach a town located 34 1/2 miles downstream from the spill?
To find the time it takes for the chemicals to reach the town, we need to divide the distance by the speed of the river.
Distance downstream = 34 1/2 miles = 34.5 miles
Speed of the river = 2 3/10 miles per hour = 2.3 miles per hour
Time = Distance / Speed
Time = 34.5 miles / 2.3 miles per hour
Time = 15 hours
Therefore, it will take the chemicals 15 hours to reach the town.
To find the time it will take for the chemicals to reach the town, we can use the formula: time = distance / speed.
1. First, convert the speed of the river from miles per hour to miles per minute. Since there are 60 minutes in an hour, we multiply the speed by 1/60:
Speed of the river = 2 3/10 mph = (2 + 3/10) mph = (20/10 + 3/10) mph = 23/10 mph
Speed of the river in miles per minute = (23/10) mph × (1/60) hpm = (23/600) mpm (approximately)
2. Next, calculate the time it takes for the chemicals to travel the distance of 34 1/2 miles downstream from the spill:
Time = Distance / Speed
Time = 34 1/2 miles / (23/600) mpm
To simplify the calculation, we can convert the mixed number to an improper fraction:
34 1/2 miles = (34 × 2 + 1) / 2 miles = 69/2 miles
Substituting the values into the formula:
Time = (69/2 miles) / (23/600) mpm
To divide fractions, we multiply by the reciprocal of the divisor:
Time = (69/2 miles) × (600/23) min/mile
Multiply the fractions:
Time = (69 × 600) / (2 × 23) min
Calculate the numerator and denominator:
Time = 41400 / 46 min
Simplify the fraction:
Time = 900 min
Therefore, it will take approximately 900 minutes for the chemicals to reach the town located 34 1/2 miles downstream from the spill.
To find out how long it will take for the chemicals to reach the town, you need to determine the time it takes for the chemicals to travel a distance of 34 1/2 miles at a rate of 2 3/10 miles per hour.
To calculate the time, you can use the formula:
Time = Distance / Rate
The given distance is 34 1/2 miles and the given rate is 2 3/10 miles per hour.
First, convert the mixed number 34 1/2 to an improper fraction:
34 1/2 = (34 * 2 + 1) / 2 = 69/2
Next, convert the mixed number 2 3/10 to an improper fraction:
2 3/10 = (2 * 10 + 3) / 10 = 23/10
Now, substitute the values into the formula:
Time = 69/2 / 23/10
To divide fractions, you multiply the first fraction by the reciprocal of the second fraction:
Time = 69/2 * 10/23
To simplify, you can cancel out common factors:
Time = (69 * 10) / (2 * 23) = 690/46 = 15
Therefore, it will take approximately 15 hours for the chemicals to reach the town.