Average speed of an aeroplane!

[wrightarya]

speed of a car!

"Jack and Mack both drive 40 km from home to work each day. One day Jack said to Mack, 'If you drive home at your usual speed, I will average 40 kmph faster than you and arrive home in 20 minutes less time.' Find Mack's speed."

Answer: 52.11kmph

Im having trouble with this problem could anyone help me out?

 

[HallsofIvy]

If you let Mack's speed be "v", what is Jack's speed in terms of v? What is the time each of them takes to drive 40 km in terms of v?

 

[wrightarya]

If you let Mack's speed be "v", what is Jack's speed in terms of v? What is the time each of them takes to drive 40 km in terms of v?

i came up with this equation:

Mack's time : 40/v
Jack's time : 40/v+40 -1/3

therefore,

40/v = 40/v+40 -1/3
i solved for v and ended up with:
v = 79.5 and 0.503

i obviously did something wrong =(

 

[HallsofIvy]

i came up with this equation:

Mack's time : 40/v
Jack's time : 40/v+40 -1/3

No. If we call Mack's speed v then Jack's speed is 40+ v. Mack's time is 40/v and Jack's time is 40/(v+ 40).

The "1/3" comes in the fact that Jack's time is 1/3 hour less than Mack's:
40/v- (40/(v+ 40))= 1/3.

therefore,

40/v = 40/v+40 -1/3

Yes, this is correct.

i solved for v and ended up with:
v = 79.5 and 0.503

i obviously did something wrong =(

Your equation is correct. How did you solve the equation?

 

[wrightarya]

No. If we call Mack's speed v then Jack's speed is 40+ v. Mack's time is 40/v and Jack's time is 40/(v+ 40).

The "1/3" comes in the fact that Jack's time is 1/3 hour less than Mack's:
40/v- (40/(v+ 40))= 1/3.


Yes, this is correct.


Your equation is correct. How did you solve the equation?

even though its incorrect, but if you insist, here's my solution ha! :-?

40/v = 120 - v + 40
40 = 120v -v^2 + 40v
v^2 - 80v +40 = 0
substitute into quadratic formula
v = 79.497 or 0.5

 

[HallsofIvy]

even though its incorrect, but if you insist, here's my solution ha! :-?

40/v = 120 - v + 40

I don't see how you got this. I would presume that after you had \(\displaystyle \frac{40}{v}- \frac{40}{v+ 40}= \frac{1}{3}\) you added \(\displaystyle \frac{40}{v+ 40}\) to both sides then combine fractions on the right:
\(\displaystyle \frac{40}{v}= \frac{40}{v+ 40}+ \frac{1}{3}\)
but the right side is then \(\displaystyle \frac{120}{3(v+ 40}+ \frac{v+ 40}{3(v+ 40)}= \frac{120+ v+ 40}{3(v+ 40)}\)
so you have two errors- first, the fraction is added, not subtracted so you have "+v", not "-v". Second you have somehow dropped the denominator on the right. Now, do you see why I wanted you to show how you attempted to solve the equation?

40 = 120v -v^2 + 40v
v^2 - 80v +40 = 0
substitute into quadratic formula
v = 79.497 or 0.5

I would, instead, starting from \(\displaystyle \frac{40}{v}- \frac{40}{v+ 40}= \frac{1}{3}\), multiply on both sides by x+ 40 to get \(\displaystyle \frac{40(v+ 40}{v}- 40= \frac{x+ 40}{3}\). Then multiply on both sides by v to get \(\displaystyle 40(v+ 40)- 40v= \frac{v(x+ 40)}{3}\). If you don't like fractions, multiply both sides by 3: \(\displaystyle 120(v+ 40)- 120v= v(v+ 40)\). That will give a quadratic equation, but not the one you have.

 

[lookagain]

*** Correction of some typos for HallsofIvy:

"I don't see how you got this. I would presume that after you had \(\displaystyle \ \frac{40}{v}- \frac{40}{v + 40}= \frac{1}{3}\) you added \(\displaystyle \frac{40}{v + 40}\) to both sides then combine fractions on the right:
\(\displaystyle \frac{40}{v}= \frac{40}{v + 40}+ \frac{1}{3}\)
but the right side is then \(\displaystyle \frac{120}{3(v + 40)}+ \frac{v+ 40}{3(v + 40)}= \frac{120 + v + 40}{3(v + 40)}\)
so you have two errors- first, the fraction is added, not subtracted so you have "+v", not "-v". Second you have somehow dropped the denominator
on the right. Now, do you see why I wanted you to show how you attempted to solve the equation?


I would, instead, starting from \(\displaystyle \frac{40}{v}- \frac{40}{v + 40}= \frac{1}{3}\), multiply on both sides by v+ 40 to get \(\displaystyle \frac{40(v + 40)}{v}- 40= \frac{v + 40}{3}\). Then multiply on both sides by v to get \(\displaystyle 40(v + 40)- 40v= \frac{v(v + 40)}{3}\). If you don't like fractions, multiply both sides by 3: 120(v + 40) - 120v= v(v + 40). That will give a quadratic equation, but not the one you have."

***


- - - - - - -- - - -- - - - - - -- - - -


For instance, you were mixing x and v variables a couple of times accidentally, and you were missing
a couple of closing parentheses.

 

[HallsofIvy]

It was the wrong color!