A cyclist traveled at 20 km/hr for 3 hours, then increased his... | Mathematics MCQ | Examoogle

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MathematicsTime, Speed and Distance

A cyclist traveled at 20 km/hr for 3 hours, then increased his speed by 10 km/hr and traveled for another 2 hours. What was his average speed (in km/hr) for the entire journey?

24 km/hr

22 km/hr

25 km/hr

23 km/hr

Correct Answer

📐 MA • Math Direct FormulaMathematicsTime, Speed and Distance

Option A

24 km/hr

Quick Summary:

Use the weighted average: Average Speed = $\frac{(s_1 \times t_1) + (s_2 \times t_2)}{t_1 + t_2}$ . Here, $\frac{(20 \times 3) + (30 \times 2)}{3 + 2} = \frac{60 + 60}{5} = 24$ .

📐MAMath SolutionDirect Formula

📋 Given

For the first part: Speed = 20 km/hr, Time = 3 hours. For the second part: Speed = 20 + 10 = 30 km/hr, Time = 2 hours.

🔢 Formula Used

Average Speed=Total DistanceTotal Time\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}Average Speed=Total TimeTotal Distance​

⚡ Exam Hall Shortcut / Speed Trick

Use the weighted average: Average Speed = $\frac{(s_1 \times t_1) + (s_2 \times t_2)}{t_1 + t_2}$ . Here, $\frac{(20 \times 3) + (30 \times 2)}{3 + 2} = \frac{60 + 60}{5} = 24$ .

⚠️ Common Student Trap / Pitfall

Students often calculate the average of the two speeds ( $\frac{20 + 30}{2} = 25$ ) instead of calculating total distance divided by total time.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate distance for both parts

First, find distance $D_1 = S_1 \times T_1 = 20 \times 3 = 60$ km. Then, find distance $D_2 = S_2 \times T_2 = 30 \times 2 = 60$ km.

D1=60 km,D2=60 kmD_1 = 60 \text{ km}, \quad D_2 = 60 \text{ km}D1​=60 km,D2​=60 km

Calculate total distance and total time

Total distance is the sum of distances, and total time is the sum of time intervals.

Total Distance=60+60=120 km,Total Time=3+2=5 hours\text{Total Distance} = 60 + 60 = 120 \text{ km}, \quad \text{Total Time} = 3 + 2 = 5 \text{ hours}Total Distance=60+60=120 km,Total Time=3+2=5 hours

Calculate average speed

Divide the total distance by total time to find the average speed.

Average Speed=1205=24 km/hr\text{Average Speed} = \frac{120}{5} = 24 \text{ km/hr}Average Speed=5120​=24 km/hr

✅

A is correct because the total distance of 120 km divided by the total time of 5 hours results in 24 km/hr.

Core Concepts Used

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Average Speed Weighted Average Total Distance vs Total Time

💡 EXAM TIP

This concept is a precursor to Relative Speed and Mixture problems, where understanding total quantity vs weighted average is essential.

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