Two towns A and B are 400 km apart. A motor cyclist travelling at an average speed of 60km/h left town A for town B at 1:20 pm. A matatu travelling at an average speed of 80km/h also left town A for town B at 2:00 pm. Calculate: a) the distance covered by the motor cyclist by 2:00pm, b) the distance from town A in km, where the matatu caught up with the motor cyclist, c) time when the matatu caught up with the motor cyclist.

Question

Asked on March 23, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-23T18:08:48.213Z

A) Calculate: i) The distance covered by the motor cyclist by 2:00 pm. Step 1: Determine the time the motor cyclist traveled until 2:00 pm. The motor cyclist left town A at 1:20 pm. The time elapsed until 2:00 pm is 2:00 pm - 1:20 pm = 40 minutes. Step 2: Convert the time to hours. 40 minutes = (40)/(60) hours = (2)/(3) hours Step 3: Calculate the distance covered by the motor cyclist. Speed of motor cyclist = 60 km/h. Distance = Speed × Time Distance = 60 km/h × (2)/(3) h Distance = 20 × 2 km Distance = 40 km The distance covered by the motor cyclist by 2:00 pm is 40 km. ii) The distance from town A in km where the matatu caught up with the motor cyclist. Step 1: Set up equations for the distance of each vehicle from town A. Let t be the time in hours from 2:00 pm when the matatu catches up with the motor cyclist. At 2:00 pm, the motor cyclist has already covered 40 km (from part i). Distance of motor cyclist from A at time t (after 2:00 pm): D_motorcyclist = 40 + 60t The matatu left town A at 2:00 pm. Distance of matatu from A at time t (after 2:00 pm): D_matatu = 80t Step 2: Equate the distances to find the time t when they meet. When the matatu catches up with the motor cyclist, their distances from town A are equal. 40 + 60t = 80t Step 3: Solve for t. 40 = 80t - 60t 40 = 20t t = (40)/(20) t = 2 hours This means they meet 2 hours after 2:00 pm. Step 4: Calculate the distance from town A where they meet. Substitute t=2 hours into either distance equation. Using the matatu's distance: D_matatu = 80t D_matatu = 80 km/h × 2 h D_matatu = 160 km The distance from town A where the matatu caught up with the motor cyclist is 160 km. iii) Time when the matatu caught up with the motor cyclist. Step 1: Use the time t calculated in part (ii). The matatu caught up with the motor cyclist 2 hours after 2:00 pm. Meeting time = 2:00 pm + 2 hours Meeting time = 4:00 pm The matatu caught up with the motor cyclist at 4:00 pm.

Accepted Answer · 2026-03-23T18:08:48.213Z

A) Calculate: i) The distance covered by the motor cyclist by 2:00 pm. Step 1: Determine the time the motor cyclist traveled until 2:00 pm. The motor cyclist left town A at 1:20 pm. The time elapsed until 2:00 pm is 2:00 pm - 1:20 pm = 40 minutes. Step 2: Convert the time to hours. 40 minutes = (40)/(60) hours = (2)/(3) hours Step 3: Calculate the distance covered by the motor cyclist. Speed of motor cyclist = 60 km/h. Distance = Speed × Time Distance = 60 km/h × (2)/(3) h Distance = 20 × 2 km Distance = 40 km The distance covered by the motor cyclist by 2:00 pm is 40 km. ii) The distance from town A in km where the matatu caught up with the motor cyclist. Step 1: Set up equations for the distance of each vehicle from town A. Let t be the time in hours from 2:00 pm when the matatu catches up with the motor cyclist. At 2:00 pm, the motor cyclist has already covered 40 km (from part i). Distance of motor cyclist from A at time t (after 2:00 pm): D_motorcyclist = 40 + 60t The matatu left town A at 2:00 pm. Distance of matatu from A at time t (after 2:00 pm): D_matatu = 80t Step 2: Equate the distances to find the time t when they meet. When the matatu catches up with the motor cyclist, their distances from town A are equal. 40 + 60t = 80t Step 3: Solve for t. 40 = 80t - 60t 40 = 20t t = (40)/(20) t = 2 hours This means they meet 2 hours after 2:00 pm. Step 4: Calculate the distance from town A where they meet. Substitute t=2 hours into either distance equation. Using the matatu's distance: D_matatu = 80t D_matatu = 80 km/h × 2 h D_matatu = 160 km The distance from town A where the matatu caught up with the motor cyclist is 160 km. iii) Time when the matatu caught up with the motor cyclist. Step 1: Use the time t calculated in part (ii). The matatu caught up with the motor cyclist 2 hours after 2:00 pm. Meeting time = 2:00 pm + 2 hours Meeting time = 4:00 pm The matatu caught up with the motor cyclist at 4:00 pm.

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