Question : A student goes to school at a speed of $5 \frac{1}{2}$ km/hr and returns at a speed of 4 km/hr. If he takes $4 \frac{3}{4}$ hours for the entire journey, then the total distance covered by the student (in km) is:
Option 1: 11
Option 2: 22
Option 3: 16
Option 4: 24
Correct Answer: 22
Solution :
Speed of students goes to school = $5\frac{1}{2} = \frac{11}{2}$ km/hr
Speed of students in returns = 4 km/hr
Time taken to complete the entire journey = $4\frac{3}{4} = \frac{19}{4}$ hours
Distance = Speed × Time
Let the distance be $D$ km.
According to the question
$\frac{D}{(\frac{11}{2})} + \frac{D}{4} = \frac{19}{4}$
$⇒\frac{2D}{11} + \frac{D}{4} = \frac{19}{4}$
$⇒\frac{(8D + 11D)}{44} = \frac{19}{4}$
$⇒\frac{19D}{44} = \frac{19}{4}$
$\therefore D = 11$
The total distance covered by the student
= Time taken to going school + Time taken to return
= (11 + 11) km = 22 km
Hence, the correct answer is 22 km.
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