SOLUTION: A ship cruising on a river can travel the 135-mile distance between two cities in 15 hours when cruising against the current. When cruising with the current,the trip takes 5 fewer
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Question 120410This question is from textbook Algebra 1
: A ship cruising on a river can travel the 135-mile distance between two cities in 15 hours when cruising against the current. When cruising with the current,the trip takes 5 fewer hours. Write and solve a system of equations to find the speed of the current and of the ship in still water. This question is from textbook Algebra 1
You can put this solution on YOUR website! A ship cruising on a river can travel the 135-mile distance between two cities in 15 hours when cruising against the current. When cruising with the current,the trip takes 5 fewer hours. Write and solve a system of equations to find the speed of the current and of the ship in still water.
:
Let x = ship speed in still water
Let y = current speed
Then
Speed upstream = (x-y)
Speed downstream = (x+y)
:
Write a distance equation for each; distance = time * speed:
15(x-y) = 135
10(x+y) = 135
:
Simplify both equations; Divide the 1st one by 15 and the 2nd one by 10:
x - y = 9
x + y = 13.5
--------------adding eliminates y, find x
2x +0y = 22.5
x = 22.5/2
x = 11.25 ship speed in still water
:
Find y using x + y = 13.5
11.25 + y = 13.5
y = 13.5 - 11.25
y = 2.25 speed of the current
:
:
Check solution:
upstream speed = 11.25 - 2.25 = 9
down stm speed = 11.25 + 2.25 = 13.5
:
Find the distances
15 * 9 = 135
and
10 * 13.5 = 135; confirms our solutions
