A cyclist travels a total distance of 90\text{ km}. She completes the first 40\text{ km} o… — JAMB UTME

A cyclist travels a total distance of $90\text{ km}$ . She completes the first $40\text{ km}$ of the journey at a constant speed of $20\text{ km/h}$ . If her average speed for the entire journey is $30\text{ km/h}$ , find her speed, in $\text{km/h}$ , over the remaining distance.

Answer: 50 km/h

Answer

The speed over the remaining distance is

50\text{ km/h}

Average speed is total distance divided by total time. For a

90\text{ km}

trip with an average speed of

30\text{ km/h}

, the total trip time is

3\text{ hours}

. Covering the first

40\text{ km}

20\text{ km/h}

requires

2\text{ hours}

, leaving

1\text{ hour}

to cover the remaining

50\text{ km}

(

90 - 40

). Dividing

50\text{ km}

1\text{ hour}

results in a required speed of

50\text{ km/h}

Step-by-Step Solution

Calculate the total time for the complete trip

Total duration =

3\text{ hours}

Average speed is defined as total distance divided by total time:

T = \frac{D}{V_{\text{avg}}} = \frac{90}{30} = 3\text{ hours}

Calculate the time spent covering the first part of the journey

Time for first segment =

2\text{ hours}

Time taken for a segment is distance divided by speed:

t_1 = \frac{40}{20} = 2\text{ hours}

Find the remaining time and remaining distance

Remaining time =

1\text{ hour}

; Remaining distance =

50\text{ km}

Subtracting the first segment's time and distance from the totals gives

3 - 2 = 1\text{ hour}

and

90 - 40 = 50\text{ km}

Calculate the required speed for the second segment

Speed for remaining distance =

50\text{ km/h}

Speed is calculated by dividing remaining distance by remaining time:

\frac{50\text{ km}}{1\text{ hour}} = 50\text{ km/h}

Key Concept

Average Rate and Speed Calculations

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