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Two bicyclists travel in opposite directions. One travels $5$ miles per hour faster than the other. In $2$ hours they are $50$ miles apart. What is the rate of the faster bicyclist?

  1. $11.25$ mph
  2. $15$ mph
  3. $20$ mph
  4. $22.5$ mph
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Ans is option (B)

Let the speed of the slower bicyclist be  $x$  miles per hour. Then the speed of faster bicyclist would be  $x+5$  miles per hour.

Using the concept of relative motion here, let’s keep the slower bicyclist at rest. Then the faster bicyclist would be traveling towards the slower bicyclist with a speed of  $x+5-(-x)=2x+5$  miles per hour.

Now, the faster bicyclist travels  $50$ miles in  $2$ hours.

$\therefore$  $2=\frac{50}{2x+5}$       ($\because$  time  $=$  distance/ speed)

$\Rightarrow$   $x=10$  miles per hour.

So, the speed of the faster bicyclist is,  $10+5=15$ miles per hour.

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