Martina leaves home at 9 AM bicycling at a rate of 24 mih Tw

Martina leaves home at 9 A.M., bicycling at a rate of
24 mi/h. Two hours later, John leaves, driving at the rate of 48 mi/h. At what time will John catch up with Martina?

Solution

Speed of Martina = 24 mph
So distance covered by her in 2 hrs = 24*2
= 48 miles
==> at 11 A.M., Martina is 48 miles away from John.
Speed of John = 48 mph
Let us say the they both meet after x hrs after John\'s departure.
Distance travelled by Martina in x hrs = 24x + 48
Distance travelled by John in x hrs = 48x
As they meet , they would have travelled the same distance.
==> 48x = 24x + 48
==> 48x - 24x = 48
==> 24x = 48
==> 24x/24 = 48/24
==> x = 2
==> they meet after 2hrs after John\'s departure.
==> they meet at 11 A.M., + 2hrs
at 1 P.M
Thus John catches up with Martina at 1 P.M