Question
Download Solution PDFA car starts from point A towards point B, travelling at the speed of 20 km/h. 1\(\frac{1}{2}\)hours later, another car starts from point A and travelling at the speed of 30 km/h and reaches 2\(\frac{1}{2}\)hours before the first car. Find the distance between A and B.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A car starts from point A towards point B, travelling at the speed of 20 km/h.
1\(\frac{1}{2}\)hours later, another car starts from point A and travelling at the speed of 30 km/h and reaches 2\(\frac{1}{2}\)hours before the first car.
Concept used:
Total distance = \(\frac{(S_1 × S_2)}{S_1-S_2} \times (T_1+T_2)\)
Here,
S1 = speed of the faster object
S2 = speed of the slower object
T1 = Time1
T2 = Time 2
Calculation:
According to the concept,
Total distance = \(\frac{(20 × 30)}{30-20} \times (1.5+2.5)\)
⇒ \(\frac{(600)}{10} \times 4\)
⇒ 240 km
∴ The distance between A and B is 240 km.
Alternate Method
Let the total distance be x km,
In 1.5 hr 1st car travel 30 km, remaining (x - 30) km
So, according to the question.
⇒ \(\frac{(x - 30)}{20} - \frac{x}{30}\) = 2.5
⇒ x - 90 = 150
⇒ x = 240 km
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