At 7 a.m. John leaves his home riding his bicycle due west, at a speed of 11 miles per hour, toward Mark's house, which is 260 miles away. Five hours later Mark leaves his home along the same route to John's house on his bicycle traveling at 9 miles per hour. At what time do they meet each other on the way?
A. 1:00 p.m.
B. 5:00 p.m.
C. 8:15 p.m.
D. 10:15 p.m.
E. 10:25 p.m.
Total Distance = 260 miles
John started his journey at 7 am.
Mark starts his journey 5 hours later, ie; at 12 noon.
Mark Speed = 9 miles/hr
John Speed = 11miles/hr
Distance traveled by John in 5 hours = 5 x 11 = 55 miles
Distance between Mark and John when Mark started his journey = 260 - 55 = 205 mile
[Relative speed = When 2 objects are moving in opposite directions with speeds x and y miles/hr, then the relative speed = (x + y) miles/ hr]Relative speed of John and Mark = 11 + 9 = 20 miles/hr
Required time taken for Mark and John to meet = Time = Distance / Relative Speed = \(\frac{205}{20}\) = 10.25 hr or 10 hr 15 mins.
Therefore Required Time =
10:15 pm Answer D..._________________
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