Algebraic Expression With 3 Variables Story Problem

[gjthompson]

Hi everyone, so this is the problem:

A bicyclist is on an aircraft carrier which is on a river.

• From shore, the bicyclist appears to be traveling at 5mph downstream.
• The sum of the speed of the carrier and the speed of the river is 2x the speed of the bicycle.
• The bicycle is going 5x faster than the river and in the opposite direction.

Find the speed of the aircraft carrier, bicycle, and the current of the river.

So I have established the variables as:
C- Aircraft carrier speed.
B-Bicycle speed.
R-current of the river.

And I think I have two equations, but correct me if they are wrong:
C+R=2B
B=5R

Now this is where I am stuck, I am not sure what the final equation is, or if the two I came up with are right, if someone could just explain how to get the three equations I would really appreciate it. Thanks!

 

[stapel]

Hi everyone, so this is the problem:

A bicyclist is on an aircraft carrier which is on a river.

• From shore, the bicyclist appears to be traveling at 5mph downstream.
• The sum of the speed of the carrier and the speed of the river is 2x the speed of the bicycle.
• The bicycle is going 5x faster than the river and in the opposite direction.

Find the speed of the aircraft carrier, bicycle, and the current of the river.

So I have established the variables as:
C- Aircraft carrier speed.
B-Bicycle speed.
R-current of the river.

And I think I have two equations, but correct me if they are wrong:
C+R=2B
B=5R

Now this is where I am stuck, I am not sure what the final equation is, or if the two I came up with are right, if someone could just explain how to get the three equations I would really appreciate it. Thanks!

This is an interesting word problem. I've never seen one quite like it before.

Thank you for clearly defining your variables. I think the reason they mention "downstream" and "opposite direction" is that we're expected to use the speeds without the directionality in some equations, and not in others. We also need to consider whether the carrier C is going with the flow R or against it. So:

. . .going with the flow:
. . . . .|C| + |R| = 2|B|
. . . . .|B| = 5|R|
. . . . .|C| + |R| - |B| = 5

Where does this lead? On the other hand, we might have:

. . .going against the flow:
. . . . .|C| + |R| = 2|B|
. . . . .|B| = 5|R|
. . . . .|C| - |R| + |B| = 5

Where does this lead? (Remember to take directionality into account.)