At an ordinary rate a man can row the distance from
Pasig to Manila, about 15km, in 5 hours less time than it
takes him to return. Could he double his rate, his time to
Manila would only be one hour less than his time to
Pasig. What is the rate of Pasig River?
If his rowing speed is r, and the river's speed is s, then since time = distance/speed,
15/(r+s) = 15/(r-s) - 5
15/(2r+s) = 15/(2r-s) - 1
Now just solve for s.
Let's assume the man's rate of rowing in km/h is "x".
According to the given information, the time it takes to row from Pasig to Manila is 5 hours less than the time it takes to row back from Manila to Pasig.
So, the time taken to row from Pasig to Manila is (15 km) / (x km/h), and the time taken to row back from Manila to Pasig is (15 km) / (x km/h) + 5.
Now, if the man were to double his rate, his time to Manila would only be one hour less than his time to Pasig.
So, the time taken to row from Pasig to Manila at that doubled rate would be (15 km) / (2x km/h), and the time taken to row back from Manila to Pasig would be (15 km) / (2x km/h) + 1.
Now, let's set up the equation based on these information:
(15 km) / (x km/h) = (15 km) / (2x km/h) + 1
To solve this equation, we can cross-multiply:
(15 km) = (15 km / (2x km/h) + 1) * (x km/h)
Multiplying both sides of the equation by (2x km/h):
(15 km) * (2x km/h) = 15 km + 2x km/h
30x km²/h = 15 km + 2x km/h
Subtracting 2x km/h from both sides:
30x km²/h - 2x km/h = 15 km
28x km²/h = 15 km
Now, divide both sides of the equation by 28:
x km²/h = (15 km) / (28)
Simplifying:
x km²/h ≈ 0.536 km
So, the rate of the Pasig River is approximately 0.536 km/h.
To solve this problem, let's assign variables to the unknown quantities involved.
Let's say the rate of the man rowing is "r" km/h (kilometers per hour), and the time it takes him to row from Pasig to Manila is "t" hours.
From the given information, we know that the time it takes the man to row from Manila to Pasig is 5 hours more than the time it takes him to row from Pasig to Manila. So, the time it takes him to row from Manila to Pasig is "t + 5" hours.
Now, let's use the formula: speed = distance/time, to express the distances in terms of rates and times.
The distance from Pasig to Manila is given as 15 km, therefore the distance from Manila to Pasig is also 15 km.
Using the formula, the time it takes to row from Pasig to Manila can be expressed as:
t = 15/r
And the time it takes to row from Manila to Pasig can be expressed as:
t + 5 = 15/r
Now, let's look at the second part of the problem. If the man were to double his rate, his time to Manila would only be one hour less than his time to Pasig.
If the rate is doubled, it becomes 2r km/h. Using the formula, the time it takes to row from Pasig to Manila at this new rate can be expressed as:
t - 1 = 15/(2r)
From this equation, we can solve for "t".
t - 1 = 15/(2r)
t = 15/(2r) + 1
Now, we can equate the expressions for "t" from the two parts of the problem:
15/r = 15/(2r) + 1
To solve for "r", let's multiply both sides of the equation by "r" * 2r to eliminate the denominators:
15 * 2r = 15 * r + r * 2r
30r = 15 + 2r^2
Rearranging the equation, we get:
2r^2 - 30r + 15 = 0
Now, we can solve this quadratic equation to find the value of "r".