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At the initial speed a lap is completed in 2 hours and 40 mins. If the speed is increased by 1km/hr that time is reduced by 6 mins. How many kilometers long is the lap?

I've been stuck on this question for hours and have gotten no where. I broke the time down to pure hours

T1 = 2.666 hrs

T2 = 2.566 hrs

And then I used the rate formula to see if I could come up with any ideas:

Change in quantity/change in time = 1/.1 = 10

But I have no ideas, am clueless on to how this would be solved. Please provide explanation

Matthew S.
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    Hint: Assuming constant speed, distance is equal to velocity times time; $$ d = vt $$ Now, we have some "default" velocity $v_0$ and the default time $\frac{8}{3}~\text{hours}$. So $$ d = v_0 \cdot \left( \frac{8}{3} ~\text{hours} \right) $$ Can you write a similar equation for the second case? The left-hand side $(d)$ stays the same. – Matti P. Jun 30 '20 at 11:43
  • You have $2$ equations. $S/v=\frac{8}{3}$, $S/v-S/(v+1)=\frac{1}{10}$, can you proceed from here? WA gives $S=\frac{616}{9},,v=\frac{77}{3}$. – Alexey Burdin Jun 30 '20 at 11:44
  • A marathon is around $42$ km long. Considering that the world record time is just over $2$ hours for an average speed of $21$ km/h, not even the world-record runner would be able to run the lap in $2$ hours $40$ minutes. – Toby Mak Jun 30 '20 at 11:56
  • Thank you guys! – Matthew S. Jul 02 '20 at 01:24

1 Answers1

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I heard from a teacher recently that it is a good idea to create a table.

             Speed (km/h)    Time (h)        Distance (km)
    Lap 1:   v               2 and 40/60     S
    Lap 2:   v + 1           2 and 34/60     S

Since $ S=S $ it follows that

$$v \cdot (160/60) = (v+1) \cdot (154/60)$$

You solve this for $v$ and then you can also find $S$.

peter.petrov
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  • I have tried it this with, but with the units I used here: x * 2.666 = (x+1) * 2.5666. But how is it possible to solve for x when it's on both sides! – Matthew S. Jun 30 '20 at 12:21
  • Well, use simple fractions, not decimal ones. And learn the usual arithmetic rules. – peter.petrov Jun 30 '20 at 12:24
  • It is literally as simple as combining the variables to one value, smh I over think things way too much! Thank you! – Matthew S. Jul 01 '20 at 12:41