Question 1160872
A man cycles to a place at 10km per hour and arrives at 1 pm. If he cycles at 15km per hour he arrives 
at the same place at 11 am. What speed must he cycle to arrive at noon ?
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<pre>
Let d be the distance to travel.


Then from the condition, you have this "time" equation

    {{{d/10}}} - {{{d/15}}} = 2  hours.


To solve this equation, multiply both sides by 30. You will get

    3d - 2d = 60,

    d       = 60.


Thus the distance is 60 kilometers.


At the rate of 15 km/h, the cyclist cover it in 4 hours and arrives at 11 am.


To arrive at noon, the cyclist shoud travel 5 hours; hence, his speed should be 60/5 = 12 kilometers per hour.    <U>ANSWER</U>
</pre>

Solved.