How to find distance provided only change in speed and change on time?

Question

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

Answer 1

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 $S$.