Help With an Algebra Question?

Question

Twilight Sparkle lefter her home heading east and Apple Jack left two hours later heading west at a rate of 5 mph faster than twilight Sparkle. Six hours later after Twilight Sparkle left, she and Apple Jack were 600 miles apart. How fast was Twilight Sparkle moving?

Answer 1

Remember Distance = Rate x Time

In this case, we know a total distance and a total time, but not the individual rates. 

Also, there are two time periods to consider: the time TS travelled alone (2 hours) and the time they both travelled (6-2, or 4 hours)

 

TS travelled at some rate (r) for 2 hours alone.  That distance = 2r

 

Then, TS travelled at r rate for 4 hours    That distance = 4r

while AJ travelled at (r+5) for 4 hours      That distance = 4(r+5) = 4r +20

 

Clearly, you add TS's distances together to get her total distance travelled:  2r + 4r = 6r

 

And, since they moved in opposite directions, you ADD AJ's distance:  6r + (4r + 20) = 10r + 20

 

The total distance, represented now by 10r+20, is given.  So  600 = 10r + 20. Subtract 20 from both sides, and divide by 10, and r = 58

 

Twilight Sparkle was moving at 58 mph.  Apple Jack at 63 mph.

(58 * 6 + 63 * 4 = 348 + 252 = 600, which confirms our calculations)