# Thread: Urgently need help with alebra problem!!

1. ## Urgently need help with alebra problem!!

Hi
My 15 year old daughter urgently needs help with two algebra problems for her year 10 maths. We would be very grateful if someone could show us how to solve the following two problems.

1)
A school is expected to plant trees along a river bank. The project is to take a certain number of days.
If they plant 240 trees per day, then they will be short by 400 trees.
If they plant 280 trees per day, they will plant 200 more than planned.
How many trees are planted, and how many days will it take?
2)A train passes a pole in 15 seconds, and in 45 seconds it passes through a tunnel 600 metres long. What is the speed of the train? How long is it?

2. Hi, jennybianca

1) Firstly we need to set up the equations.

$\displaystyle Let~D~=~Number~of~Days~~~,~~~P~=~Total~Planned~Tre es$

"If they plant 240 trees per day, then they will be short by 400 trees."

So;

$\displaystyle 240D~=~P-400~~~[1]$

"If they plant 280 trees per day, they will plant 200 more than planned."

So;

$\displaystyle 280D~=~P+200~~~[2]$

No solve $\displaystyle [1]$ and $\displaystyle [2]$ simultaneously.

$\displaystyle [1]~~~P~=~240D+400$

$\displaystyle [2]~~~P~=~280D-200$

Thus,

$\displaystyle 240D+400~=~280D-200$

$\displaystyle \implies~40D~=~600$

$\displaystyle \implies~D~=~15$

Now sub into either $\displaystyle [1]$ or $\displaystyle [2]$ to find out how many trees planned ($\displaystyle P$)

2) We have $\displaystyle Time~=~t~=~45s~~~,~~~Distance~=~d~=~600m$

Now use the formula $\displaystyle s~=~\frac{d}{t}$ (where s is the speed of the train)

$\displaystyle s~=~\frac{600}{45}$

$\displaystyle \implies~s~=~\frac{40}{3}~\approx~13.33$

Now because we have metres over second the unit is metre per second $\displaystyle (ms^{-1})$

Thus the speed of the train is $\displaystyle \frac{40}{3}ms^{-1}~\approx~13.33ms^{-1}$

Now assuming the width of the pole is negligible and the train has constant speed, the same formula can be used;

$\displaystyle s~=~\frac{d}{t}$

$\displaystyle \implies~d~=~st$

$\displaystyle \implies~d~=~\frac{40}{3}\cdot15$

$\displaystyle \implies~d~=~200$

Thus the length of the train is $\displaystyle 200m$

3. This is fantastic. I showed my daughter your response & it helped her a great deal. The way you explained it & set it out is very professional. Thank you very much.