A canoe in still water travels at a rate of 10 miles per hour. The current today is traveling at a rate of 3 miles per hour. If it took an extra hour to travel upstream, how far was the trip one way?
about 14 miles
about 15 miles
about 16 miles
about 17 miles
About 15 miles is the answer
d/(10-3) = d/(10+3)+1
so you are correct
To find the distance of the one-way trip, we need to understand the relationship between the speed of the canoe and the speed of the current.
Let's assume the distance of the one-way trip is "D" miles.
When the canoe is traveling upstream, it has to work against the current, so its effective speed would be the speed of the canoe minus the speed of the current. In this case, the effective speed can be calculated as 10 mph (speed of the canoe) - 3 mph (speed of the current) = 7 mph.
We know that it took an extra hour to travel upstream, which means the time taken for the upstream trip is one hour more than the time taken for the downstream trip.
Let's assume the time taken for the downstream trip is "T" hours. So, the time taken for the upstream trip would be "T + 1" hours.
We can use the formula speed = distance / time to connect the speed, distance, and time for both trips.
For the downstream trip:
10 mph = D miles / T hours
For the upstream trip:
7 mph = D miles / (T + 1) hours
To solve this problem, we can use the method of substitution or rearrange the equations.
Let's use the method of substitution.
From the first equation, we can express T as D/T.
Substituting this value of T in the second equation, we get:
7 mph = D miles / (D/T + 1) hours
Simplifying the equation:
7 mph = D miles / (D + T) / T
Multiplying T on both sides:
7 mph * T = D miles / (D/T + 1)
Multiplying both sides by (D/T + 1):
7 mph * T * (D/T + 1) = D miles
Simplifying further:
7mph * D + 7mph * T = D miles
Moving all D terms to one side and T terms to the other side:
7mph * D - D miles = -7mph * T
Factoring out D:
D * (7mph - 1) = -7mph * T
Dividing both sides by (7mph - 1):
D = (-7mph * T) / (7mph - 1)
Substituting the given values:
D = (-7 * 10 * T) / (7 - 1)
D = (-70 * T) / 6
Now, let's try different values of T and see which option matches the calculated distance D.
If we substitute T = 2 in the equation, we get:
D = (-70 * 2) / 6
D = -140 / 6
D ≈ -23.33 miles
Since distance cannot be negative, we can rule out option one.
If we substitute T = 3 in the equation, we get:
D = (-70 * 3) / 6
D = -210 / 6
D ≈ -35 miles
Again, distance cannot be negative, so we can rule out option two.
If we substitute T = 4 in the equation, we get:
D = (-70 * 4) / 6
D = -280 / 6
D ≈ -46.67 miles
This is still a negative value, so we can rule out option three as well.
If we substitute T = 5 in the equation, we get:
D = (-70 * 5) / 6
D = -350 / 6
D ≈ -58.33 miles
This is also negative, ruling out option four.
From these calculations, it seems like none of the options provided match the calculated distance D. Please double check the options or the given information provided in the question.