Emily rows six miles downstream in 1 hour and her friend Ashley,rowing 1 mile per hour faster,completes the return trip in 2 hours.
1.Find the speed of the current(c) and each girls rowing speed.
2.If Emily and Ashley were rowing separately,who would complete their trip first and by how long?Round to the nearest hundredth,if necessary.
if emily's speed is s and the river current speed is r,
1(s+r) = 6
2(s-r) = 6
s + r = 6
2s - 2r = 6
4s = 18
s = 4.5
r = 1.5
So,
Emily's speed is 4.5 mph
Ashley's speed is 5.5 mph
The river's speed is 1.5 mph
Rowing separately,
Emily's time is 6/(4.5+1.5) + 6/(4.5-1.5) = 3 hours
Ashley's time is 6/(5.5+1.5) + 6/(5.5-1.5) = 2.357 hours
Ashley finishes 0.64 hours sooner
To solve this problem, we can use the formula:
Distance = Speed × Time
Let's assume that Emily's rowing speed is E mph, Ashley's rowing speed is A mph, and the speed of the current is C mph.
1. Find the speed of the current (C) and each girl's rowing speed:
We'll start by setting up two equations with the given information.
For Emily's trip downstream:
Distance = Speed × Time
6 miles = (E + C) mph × 1 hour
For Ashley's return trip:
Distance = Speed × Time
6 miles = (A - C) mph × 2 hours
Now we need to solve these two equations simultaneously to find the values of E, A, and C.
Equation 1: 6 = (E + C)
Equation 2: 6 = 2(A - C)
Let's simplify Equation 1 and Equation 2:
Equation 1: E + C = 6
Equation 2: 2A - 2C = 6
We can rearrange Equation 2 to isolate A:
2A - 2C = 6
2A = 2C + 6
A = (2C + 6)/2
A = C + 3
Now we substitute the value of A into Equation 1:
E + C = 6
E + C = 6
E = 6 - C
Now we have three equations:
E = 6 - C
A = C + 3
E + C = 6
We can substitute the values of C and A into the third equation:
(6 - C) + C = 6
6 - C + C = 6
6 = 6
This equation is always true, which means there are an infinite number of solutions to this problem. The values of C, E, and A can be any numbers that satisfy the given conditions. Therefore, we cannot determine the exact values of the speed of the current (C) and each girl's rowing speed (E and A) without further information.
2. If Emily and Ashley were rowing separately, who would complete their trip first and by how long?
Since we don't have the specific values for their rowing speeds, we cannot determine who would complete their trip first or by how long without further information.