Math problem

[Dencology]

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two cyclist start biking from a trials start 3 hrs apart. the 2nd cyclist travels at 10 miles per hour and starts three hrs after the first cyclist who is traveling at six miles per hour. how much time will pass before the second cyclist catches up with the the first from the time the second cyclist started biking?

a. two hrs
b. 4 1/2
c. 5 3/4

ans is B.

i get 5.6 hrs. basically what i did was 6t + 10(t-3)=60 ( i got a common divisible num. here)

so from here we get 16t =90 t=5.62

2. if steve can mix 20 drinks in five min. sue can mix twenty drinks in ten min. and jack can mix twenty drinks in fifteen mintues, how much time will it take all three of them working together to mix the twenty drinks?
ans. A how?

3. druing a five day festival, a number of visitors tripled each day. if the festival opened on a thur. with 345, what was the attendance on sunday? what is the fasted way to do this? multiplying is just a no brainer. anyone with a technique?

 

[Mamona]

1. I think B is correct
After 3 hours the first cyclist has travel 18miles, while the second cyclist traveled 0. So

Equation
y=6t + 18 cyclist 1
y= 10t cyclist 2

10t = 6x + 18
4t = 18
t= 4.5

 

[bigasianpianist]

For 2, you divide all the drinks by the amount of time it takes for the corresponding person, and then you just guesstimate the time, so i would say between two to three minutes total for twenty drinks, closer to 3.

 

[kush87]

#3

Thursday Friday Saturday Sunday
( 345 X 3 ) X 3 ) X 3)

= 345 X 3 X 3 X 3
= 345 X 27
= 9315

 

[klutzy1987]

1) 10x=6(x+3)
4x=18
x=4.5

 

[klutzy1987]

2)
(120/30)+(60/30)+(40/30)=(20/x)
220/30=20/x
x=600/220
x=2.72 min

 

[klutzy1987]

3)
345*(3*3*3)
345*27=9315

You have to multiply it out. There is no other way.

 

[TheGreenWave]

klutzy has the answers right, but Im going to ellaborate on #1 to see if it helps you understand these types of problems.

The easiest way to think about it (IMO), is by using the concept of relative velocity. Basically how fast is the faster cyclist going in terms of the slower cyclist.

-First, remember that in the three hours the 1st cyclist has gone 18 miles (6 X 3)
-So when the 2nd cyclist starts he/she has to make up 18 miles (basically this is the distance they need to travel)
-Now calculate how fast the 2nd cyclist is going compared to the first. to do this just subtract the speed of the 1st cyclist from the 2nd; 10mph - 6mph = 4mph
-Now what you have is the 2nd cyclist traveling at 4mph (relative velocity) trying to catch a fixed point 18 miles away (b/c relative to this speed, the other cyclist is not moving)
- 4mph X time = 18 miles
-time = 4.5

hope that is useful

 

[Dencology]

TheGreenWave, i have difficulty with percent problems. like a problem so simple really hammers me down: check it out: i am sure it is easy for you:
jum is able to sell a hand carved statue for 670 which was a 35% profit over his cost. how much did the statue originally cost him?
The green wave, you explained well. thanks.

 

[TheGreenWave]

TheGreenWave, i have difficulty with percent problems. like a problem so simple really hammers me down: check it out: i am sure it is easy for you:
jum is able to sell a hand carved statue for 670 which was a 35% profit over his cost. how much did the statue originally cost him?
The green wave, you explained well. thanks.

Here are some pointers for these types of problems (btw sometimes these are worded poorly).
- profit = sell price - cost
-% profit = profit / cost
-So if jim sells at a price of 670 and the %profit was 35, you have enough info to solve.
- combine both these formulas like so: sell price - cost = profit = cost X & profit
- plug in the numbers : 670 - cost = cost X .35
- 670 / .35 - cost/.35 = cost
- the rest is just simple algebra (hint: use 35/100 instead of 35 and its easy)

Answer = $500

 

[kush87]

TheGreenWave, i have difficulty with percent problems. like a problem so simple really hammers me down: check it out: i am sure it is easy for you:
jum is able to sell a hand carved statue for 670 which was a 35% profit over his cost. how much did the statue originally cost him?
The green wave, you explained well. thanks.

35% profit over his cost.

if you do 0.35 X (some value) then you would get 35 % of that value
but if you do 1.35 X (some value) then you would get 35% on top of that value

Example:
35% of his cost (lets say $ 100)
then 0.35 x $100 = $35 (35 % of 100)


35% profit over his cost
then 1.35 x $100 = $135 (this is 35% more than the cost)

So for you question you would set up the equation like this

1.35(cost) = 670 (you multiply by 1.35 because its 35% on TOP of the cost)
then cost = 670/1.35 = ~496