Question

At 11.00 a.m. a man started cycling from Newcastle to Hexham, 30 krn away. He
rode at a steady 10 km/h. He stopped for 30 minutes at 12.30 pm to have lunch
and then resumed his journey at the same steady speed. A car left Hexham for
Newcastle at 11.30 a.m. doing a steady speed of 50 km/h on the same road as the
cyclist. Draw a distance time graph to show the two journeys and use it to find the
approximate time and place at which the car and the cyclist passed each other.

Answer 1

The cyclist and the car will intersect at 11:50 AM.

To determine the approximate time and place at which the car and the cyclist passed each other the following calculation must be performed:

-The advance of each of the parts must be calculated, and the point where said movement coincides.

• Cyclist =  
• Point 0 at 11:00 A.M. --- Stops at 12:30 P.M. having circulated at 10 km / h, that is, it traveled about 15 km (12:30 - 11:00 = 1:30 (1.5)).
• After half an hour of rest, it continues on its way from 1:00 p.m., arriving at its destination at 2:30 p.m.
• If in 60 minutes it travels 10 km, in 6 minutes it travels 1 km, and per minute it travels 0.16 km.

• Car =  
• Point 0 at 11:30 AM --- Speed ​​of 50 km / h
• In half an hour it travels 25 km. In 6 minutes it travels 5 km, and per minute it travels 0.83 km. In total it takes 36 minutes to reach Newcastle at 12:06 P.M.

• 11:30 =
• Cyclist = 30 - 10 = 20
• Car = 0  
• 11:36 =
• Cyclist = 20 - 1 = 19
• Car = 5  
• 11:42 =
• Cyclist = 18
• Car = 10  
• 11:48 =
• Cyclist = 17
• Car = 15  
• 11:49 =
• Cyclist = 17 - (1/6) = 16.83
• Car = 15 + (5/6) = 15.83  
• 11:50 =
• Cyclist = 16.83 - (1/6) = 16.66
• Car = 15.83 + 0.83 = 16.66

Therefore, the cyclist and the car will intersect at 11:50 AM.

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