Abby rows 10 km upstream and 10 km back in a total time of 3 hr. The speed of the river is 5km/h. Find Abby’s speed in still water.
she went the same distance.
(v+5)3=(v-5)10)
3v+15=10v-50
7v=65
v=65/7 km/hr
What does this have to do with quadratics?
thats what my mathbook said. That why I needed help thank you bobpursley.
To find Abby's speed in still water, we can set up an equation based on the information given.
Let's assume Abby's speed in still water is represented by the variable 's' (in km/h).
We know that Abby rows 10 km upstream (against the current) and 10 km downstream (with the current). The speed of the river is given as 5 km/h.
When Abby rows upstream, her effective speed relative to the ground will be s - 5 km/h (since she has to row against the current). Similarly, when she rows downstream, her effective speed relative to the ground will be s + 5 km/h (since she has the assistance of the current).
We are given that Abby completes the round trip (upstream and downstream) in a total time of 3 hours. This means the time taken for the upstream journey plus the time taken for the downstream journey is equal to 3 hours.
Let's break down the time taken for each part of the journey. The time taken to row upstream can be calculated as distance/speed, so the time taken for the upstream journey would be:
10/(s - 5) [distance/speed]
Similarly, the time taken to row downstream would be:
10/(s + 5) [distance/speed]
According to the given information, the total time for the round trip is 3 hours:
10/(s - 5) + 10/(s + 5) = 3
Now, we have an equation with one variable (s), which we can solve to find Abby's speed in still water.
To solve this equation, we can start by multiplying both sides by (s - 5)(s + 5) to eliminate the denominators:
10(s + 5) + 10(s - 5) = 3(s - 5)(s + 5)
Simplifying:
10s + 50 + 10s - 50 = 3(s^2 - 25)
Combine like terms:
20s = 3s^2 - 75
Rearrange the equation:
3s^2 - 20s - 75 = 0
This is a quadratic equation, which can be factored or solved using the quadratic formula. Solving this equation will give us the value(s) for 's', representing Abby's speed in still water.