use the answer provided to back into the answer. I.e. Start with the middle value and see whether you should go higher or lower.

I started with 24km and with 24km/hr it will take 60 minutes to arrive. Since this is 5 minutes late, I subtract 5 minutes from 60 to get a desired time of 55 minutes. The desired time is the same for both trials.

Since I know my desired time is 55 minutes, and that with a 25% increase in speed, which is 30km/hour, then I need to be 4 minutes quicker than my desired time, or actual time of 51 minutes at 30 km/hour. Divide 30 into 24 and you get .8hours or 48 minutes. The difference between my desired time of 55 minutes and 48 minutes is 7 minutes which is too great.

I know that Distance= Rate x Time and rearranged, Time = Distance/Rate. I know that my Time needs to get smaller and the only way to do that is to decrease the numerator or increase the Denominator. Since our rate is given (30 km/hour) I can't increase my denominator and therefore must decrease my numerator, Distance. Therefore move onto to a smaller distance.

The answer is 18. Work out the same way as desrcibed above.

***** You can solve this using alegbra too

24km/hour = 24km/60 minutes = 2/5 km/min=.4km/min

30 km/hour= 30km/60 minutes = 1/2 km/min=.5km/min

Distance is unknown X

Desired time is unknown y

1) X/2/5= y +5

2) X/1/2= y -4

Solve for y using either equation

(using no. 2) y= X/1/2 + 4

Substitute for y, X/2/5= y + 5, X/2/5= X/1/2 + 4 + 5

Convert Fractions 5x/2 (or 2.5) = 2X + 9

Subtract 2x from both sides = 2.5X-2X = 9, .5x=9

Multiply both sides by 2,

x=18km

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There are three things in life: Price, Quality, and Speed. You only get two out of the three.