Kaushal travelled for 2 hours 45 minutes at the speed of 32 km... | Mathematics MCQ | Examoogle

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MathematicsTime, Speed and Distance

Kaushal travelled for 2 hours 45 minutes at the speed of 32 km/h. At what speed (in km/h) should he travel to cover the same distance in 4 hours?

Correct Answer

📐 MA • Math Ratio MethodMathematicsTime, Speed and Distance

Option C

Quick Summary:

Use the inverse proportionality of speed and time: $\frac{v_2}{v_1} = \frac{t_1}{t_2}$ . Since $t_1 = 2.75$ and $t_2 = 4$ , $v_2 = 32 \times \frac{2.75}{4} = 8 \times 2.75 = 22$ .

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📐MAMath SolutionRatio Method

📋 Given

Initial time t1 = 2 hours 45 minutes = 2.75 hours, Initial speed v1 = 32 km/h, Target time t2 = 4 hours.

🔢 Formula Used

d=v×t,v1×t1=v2×t2d = v \times t, \quad v_1 \times t_1 = v_2 \times t_2d=v×t,v1​×t1​=v2​×t2​

⚡ Exam Hall Shortcut / Speed Trick

Use the inverse proportionality of speed and time: $\frac{v_2}{v_1} = \frac{t_1}{t_2}$ . Since $t_1 = 2.75$ and $t_2 = 4$ , $v_2 = 32 \times \frac{2.75}{4} = 8 \times 2.75 = 22$ .

⚠️ Common Student Trap / Pitfall

Many students fail to convert 45 minutes into decimal hours correctly (i.e., 0.75 hours), leading to errors when calculating the total time.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Convert time to decimal hours

Convert 2 hours 45 minutes into hours: $45 \text{ minutes} = \frac{45}{60} \text{ hours} = 0.75 \text{ hours}$ . Total time $t_1 = 2 + 0.75 = 2.75 \text{ hours}$ .

t1=2.75 hourst_1 = 2.75 \text{ hours}t1​=2.75 hours

Calculate total distance

Calculate distance $d$ using the formula $d = v \times t$ . Substituting the given values: $d = 32 \times 2.75$ .

d=32×2.75=88 kmd = 32 \times 2.75 = 88 \text{ km}d=32×2.75=88 km

Determine required speed

Calculate the speed $v_2$ required to cover distance $d = 88 \text{ km}$ in $t_2 = 4 \text{ hours}$ using $v_2 = \frac{d}{t_2}$ .

v2=884=22 km/hv_2 = \frac{88}{4} = 22 \text{ km/h}v2​=488​=22 km/h

✅

C is correct because the distance covered is 88 km, and dividing this distance by 4 hours results in a speed of 22 km/h.

Core Concepts Used

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Time-Distance formula Fraction to decimal conversion Inverse proportionality

💡 EXAM TIP

This inverse relationship between speed and time is the foundation for solving 'work and time' problems where the amount of work done is constant.

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