Maths help Watch

liverpoolteeth
Badges: 2
Rep:
?
#1
Report Thread starter 4 weeks ago
#1
Hi,


sorry to crash the thread but i'm currently really stuck on a maths based question.

could anyone show me how to work out this question in a simple way without dividing and mulitipying by large decimal numbers.

Two cars set off from the same point, at the same time, to travel the same 140 mile journey.The first car travels at 52 mph and the second car travels at 38 mph.Will there be more than an hour or less than an hour between the arrival times of the two cars?

thanks
0
reply
Will_W
Badges: 8
Rep:
?
#2
Report 4 weeks ago
#2
Use the formula speed = distance / time rearrange the equation to make time the subject as that is what you want to work out.

substitue in the values for speed and distance for both cars to work out the length of their journey.

Compare the length of the journey for both cars. You should then know if there is more than an hour or less than an hour between the arrival times of both cars.
0
reply
liverpoolteeth
Badges: 2
Rep:
?
#3
Report Thread starter 4 weeks ago
#3
Thanks for the reply.

I figured you could do it that way but i was curious to see if it could be done any other way with out having to use a calculator?
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#4
Report 4 weeks ago
#4
(Original post by liverpoolteeth)
Thanks for the reply.

I figured you could do it that way but i was curious to see if it could be done any other way with out having to use a calculator?
Sure. Just some basic mental maths is required.

Time first car takes to travel the distance: \dfrac{140}{52} = 2 + \dfrac{36}{52} = 2 + \dfrac{9}{13}

Time second car takes to travel the distance: \dfrac{140}{38} = 3 + \dfrac{26}{38} = 3 + \dfrac{14}{19}


The time difference is  \left( 3 + \dfrac{14}{19} \right) - \left( 2 + \dfrac{9}{13} \right) = 1 + \dfrac{14}{19} - \dfrac{9}{13}

So you just need to know whether the fractional part, \dfrac{14}{19} - \dfrac{9}{13}, is positive or negative.

If positive, then the time difference is greater than 1 hour.
If negative, then the time difference is less than 1 hour.

Again, using basic fraction rules, we have that: \dfrac{14}{19} - \dfrac{9}{13} = \dfrac{(14)(13)-(9)(19)}{(19)(13)}.

So the question reduces to whether the numerator is +ve or -ve.

14 \cdot 13 = (13+1)(13) = 13^2 + 13 = 169 + 13 = 182
9 \cdot 19 = (9)(10+9) = 90 + 81 = 171

So (14)(13)-(9)(19) = 11, which is positive, hence the time difference is greater than 1 hour.

But TBH, just use a calculator if you can!
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Bath
    Undergraduate Virtual Open Day Undergraduate
    Sat, 23 Feb '19
  • Ravensbourne University London
    School of Design, School of Media Further education
    Sat, 23 Feb '19
  • Leeds Trinity University
    PGCE Open Day Further education
    Sat, 23 Feb '19

Is the plastic tax enough to protect the environment?

Yes (13)
5.6%
No (219)
94.4%

Watched Threads

View All
Latest
My Feed