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Math Help - Distance Time word problem

  1. #1
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    Distance Time word problem

    Hi Guys,

    I am having trouble figuring out this distance time word problem. I created a table and show my reasoning below but I am getting some weird answers. Can you guys please point out where I am going wrong? Thanks.

    A car leaves town X at 0800 and arrives at town Y at 0915. During the first hour of the journey, the car travels at a constant speed of 80 km/h. If the average speed of the car between 0815 and 0915 is 2 km/h less than the average speed for the whole journey, find
    (a) the distance of the journey from town X to town Y,
    (b) the average speed between 0815 and 0915.

    Here's my reasoning. I figured that if I assume x is the speed between 0900 to 0915 and then using the condition part of 2nd sentence, I would be able to solve for x. Here's the table I built,

    <br />
\begin{tabular}{| l | c | c | c |}<br />
Duration & Speed(km/h) & Time(h) & Distance(km) \\<br />
0800-0900 & 80 & 1 & 80 \\<br />
0800-0815 & 80 & 1/4 & 20 \\<br />
0815-0900 & 80 & 3/4 & 60 \\<br />
0900-0915 & x & 1/4 & x/4 \\<br />
0815-0915 & 60 + x/4 & 1 & 60 + x/4 \\<br />
\end{tabular}<br />

    Then, Avg Speed is

    <br />
\begin{math}<br />
\frac{80 + (60 + \frac{x}{4})}{\frac{5}{4}} = \frac{560 + x}{5}<br />
\end{math}<br />

    And given,

    <br />
\frac{560 + x}{5} - \frac{60+x}{4} = 2<br />

    Solving that equation gives me x = 1900 km/h!!!

    Please help!, Where am I going wrong?

    P.S. First time using this Latex stuff , Thanks to great tutorial here.
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by mathguy80 View Post
    Hi Guys,

    I am having trouble figuring out this distance time word problem. I created a table and show my reasoning below but I am getting some weird answers. Can you guys please point out where I am going wrong? Thanks.

    A car leaves town X at 0800 and arrives at town Y at 0915. During the first hour of the journey, the car travels at a constant speed of 80 km/h. If the average speed of the car between 0815 and 0915 is 2 km/h less than the average speed for the whole journey, find
    (a) the distance of the journey from town X to town Y,
    (b) the average speed between 0815 and 0915.

    Here's my reasoning. I figured that if I assume x is the speed between 0900 to 0915 and then using the condition part of 2nd sentence, I would be able to solve for x. Here's the table I built,

    ...
    1. Draw a sketch (see attachment).

    2. Let x denote the distance which is traveled between 0900 and 0915. Then the average speed of the whole trip is:

    v = \dfrac{80+x}{\frac54}

    3. The average speed between 0815 and 0915 is 2\ \frac{km}h less than v:

    \dfrac{60+x}1=\dfrac{80+x}{\frac54}-2

    4. Solve for x.
    Attached Thumbnails Attached Thumbnails Distance Time word problem-durchschn_geschwindkt.png  
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  3. #3
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    Hi @earboth

    Thanks for your help. Sorry had some internet problems and wasn't able to get back to this sooner.

    I tried it your way using x as distance. And it solves correctly! I am wondering if there is any particular reason you thought of using distance instead of speed as the variable? Using distance solves much cleaner.

    Thanks.
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