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.
10
To solve this problem, let's assign variables to the unknown speeds. Let's call the speed going downstream "S" and the speed going upstream "S-2".
We know that distance = speed × time.
When Cassius drives upstream for 30 minutes, the distance covered is 30/60 × (S-2) = (1/2)(S-2) miles.
When Cassius drives downstream for 15 minutes, the distance covered is 15/60 × S = (1/4)S miles.
Since the distance covered upstream and downstream is the same, we can equate the two expressions:
(1/2)(S-2) = (1/4)S
We can now solve for S, the speed going downstream:
S/2 - 1 = S/4
2S - 4 = S
Simplifying the equation, we find:
S = 4
Therefore, Cassius's downstream speed is 4 miles per hour.
Now, we can find his upstream speed by substituting the value of S into one of our expressions:
(1/2)(4-2) = 1
Therefore, Cassius's upstream speed is 2 miles per hour.
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