Cassius drives his boat upstream for
30 minutes. It takes him
15 minutes to return downstream. His speed going upstream is two miles per hour slower than his speed going down stream. Find his upstream and downstream speed.
Julian rides his bike uphill for 45 minutes, then turns around and rides back downhill. It takes him 15 minutes to get back to where he started. His uphill speed is 3.2 miles per hour slower than his downhill speed. Find Julian’s uphill and downhill speed.
Downstream 9 upstream 6
To find Cassius's upstream and downstream speed, let's set up a system of equations.
Let's say Cassius's downstream speed is represented by the variable "x" miles per hour.
According to the problem, his upstream speed is two miles per hour slower than his downstream speed. Therefore, his upstream speed can be represented by "x - 2" miles per hour.
We know that speed = distance / time, and since we are given the time it took for each leg of the trip, we can use this formula to set up our equations.
For the upstream trip:
(x - 2) mph = distance / 0.5 hours
For the downstream trip:
x mph = distance / 0.25 hours
Since the distance traveled upstream and downstream is the same, we can equate the distance in both equations.
(x - 2) mph * 0.5 hours = x mph * 0.25 hours
Simplifying the equation:
(0.5x - x) mph = 0.25x mph
0.5x - x = 0.25x
0.25x = 0.5x
Subtracting 0.25x from both sides:
0.25x = 0
This implies that x = 0.
However, it doesn't make sense for the downstream speed to be 0. Therefore, there might be an error in the problem itself, or some missing information. Please double-check the problem statement to ensure that all the necessary details are provided.
let the downstream speed by x mph
then the upstream speed is x-2 mph
let the distance gone either way be d miles
time to go upstream = d/(x-2)
time to go downstream = d/x
but the time to go upstream is twice that of going downstream, 30 min vs 15 min
d/(x-2) = 2d/x
divide out the d
1/(x-2) = 2/x
2x-4=x
x = 4
His speed downstream is 4 mph and his upstream speed is 2 mph