# market problem

• Sep 26th 2010, 04:46 PM
kingman
market problem
Dear Sir
I would be grateful if you can help me to solve the the below questions

Last Monday, Danny walked from home to market. For the first 5 minutes, he was walking at an average speed of 35m/min. When he realized that he was going to be late by 4 minutes, he quickly increased his speed by 10m/min. As a result, he was early by 2 minutes. Find the distance between market and home.

thanks
Kingsman
• Sep 27th 2010, 12:19 AM
HappyJoe
Let the distance to the market be $x$.

The distance travelled in the first 5 minutes is:

35 m/min * 5 min = 175 m.

So after having travelled these 175 meters, the distance left is $x-175 m$.

First of all, if he continued to walk at an average speed of 35 m/min, then the time spent would be

$\frac{x}{35 m/min}$.

But since he increases his speed by 10 m/min on the last distance of x-175 m, the actual time is

$5 min + \frac{x-175 m}{45 m/min}.$

You are being told that this actual time is 2 minutes less than the time

$\frac{x}{35 m/min}-4 min.,$

so you just need to solve the equation

$5 min + \frac{x-175 m}{45 m/min} + 2 min = \frac{x}{35 m/min}-4 min.$

for $x$.

I get $x = 1120 m.$, but check that I'm right.
• Sep 27th 2010, 01:34 PM
Wilmer
Problem can be simply stated this way:
time of distance D travelled @ 35 - time of distance D travelled @ 45 = 6
So:
D/35 - D/45 = 6
D = 945

Proof:
945/35 = 27
945/45 = 21
• Sep 27th 2010, 02:29 PM
Quote:

Originally Posted by kingman
Dear Sir
I would be grateful if you can help me to solve the the below questions

Last Monday, Danny walked from home to market. For the first 5 minutes, he was walking at an average speed of 35m/min. When he realized that he was going to be late by 4 minutes, he quickly increased his speed by 10m/min. As a result, he was early by 2 minutes. Find the distance between market and home.

thanks
Kingsman

Danny travels from home to point "x".
He covers 175 meters in getting to "x".

If he increases his speed to 45m/minute, he will get to the market 6 minutes faster than if he continues at 35m/minute.

$\frac{Distance}{av.\ speed}=time\Rightarrow\ longer\ time-shorter\ time=6\ mins$

$\Rightarrow\frac{D}{slower\ speed}-\frac{D}{faster\ speed}=6$

$\Rightarrow\frac{D}{35}-\frac{D}{45}=6\Rightarrow\frac{45D-35D}{35(45)}=6$

$\Rightarrow\ 10D=(6)(35)(45)\ metres$

"D" is the distance from "x" to the market, so the distance from home to market is 175+D metres.
• Sep 27th 2010, 04:44 PM
kingman
market problem
Dear Sir.
Thanks very much for the solution but I wonder whether this problem can
be solved by just taking advantage of the fact that the relative increase in speed
of 10 m/min is given ; in doing so I suspect we can arrive at a simple equation to
solve.
Thanks very much

Kingman
• Sep 27th 2010, 06:00 PM
Quote:

Originally Posted by kingman
Dear Sir.
Thanks very much for the solution but I wonder whether this problem can
be solved by just taking advantage of the fact that the relative increase in speed
of 10 m/min is given ; in doing so I suspect we can arrive at a simple equation to
solve.
Thanks very much

Kingman

Imagine Danny and a friend together at the 175 mile mark.
They left home together travelling at 35 meters/min

At the faster speed, Danny will be at the market first.
Imagine the other person travelling at his original speed.
Danny will be waiting 6 minutes for that person to join him at the market.

Therefore that person needs to cover 6(35)=210 meters.

So Danny will have reached the market 210 meters in front of that person.

Since they parted, the friend will have travelled "y" meters when Danny reaches the market.

That distance is $y=\displaystyle\frac{35}{10}210=735\ meters$
• Sep 28th 2010, 03:55 AM
kingman
Dear Sir,
Thanks for the answer but I wonder how come there are two different answers.
thanks
• Sep 28th 2010, 04:28 AM
Wilmer
Read Archie's solution again...carefully: 735 + 210 = 945
• Sep 28th 2010, 07:25 PM
kingman
Dear Sir,
Thanks for the solution but I find difficulty following your reasoning and the answer is 1120m.
Thank you
• Sep 28th 2010, 07:53 PM
Wilmer
Quote:

Originally Posted by kingman
Dear Sir,
Thanks for the solution but I find difficulty following your reasoning and the answer is 1120m.
Thank you

YES, 1120m TOTAL: 945 + 175 = 1120
We DID state we were doing the part following the first 175m.