Question

A car started from Town P and travelled towards Town Q at 70 km/h. At the same time a van started
from Town Q and travelled to Town P at 60 km/h. After 11/4 hours, they were 65 km apart, still travelling
towards each other.What is the distance between the two towns?​ After how many hours of travel would they cross each other?​

Answer 1

$\dagger\huge\mathfrak{Solution}$

$\mathrm\green{Given :}$

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$\ast\mathtt\blue{ V_{car} = 70km/h}$

$\ast\mathtt\blue{ V_{van} = 60km/h}$

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$\ast\mathtt{After \dfrac{11}{4} h \: they \:were \:65km\: apart}$

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$\centering\mathtt\green{To\:\:Find:}$

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$\ast\mathtt\blue{ Distance \:between \:town \:P and \:Q}$

$\ast\mathtt\blue{ Time \:taken \:by \:car\:and \:van \:to\:cross\:over}$

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$\mathtt\green{Solution}$

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${\blue{\overline{\underline{\bf {\mathrm{\red{For\:Car\:P}}}}}}}$

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$\longmapsto\mathtt{ Distance = speed × time}$

$\longmapsto\mathtt{ D = 70 × \dfrac{11}{4}}$

$\longmapsto\mathtt{ D = \dfrac{385}{2}}$

$\longmapsto\mathtt{ D = 192. 5 km}$

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${\blue{\overline{\underline{\bf {\mathrm {\red{For\:Car\:Q}}}}}}}$

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$\longmapsto\mathtt{ Distance = speed × time}$

$\longmapsto\mathtt{ D_{2} = 60 × \dfrac{11}{4}}$

$\longmapsto\mathtt{ D_{2} = 15 × 11}$

$\longmapsto\mathtt{ D_{2} = 165 km}$

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${\blue {\overline{\underline {\bf {\mathrm{\red{Distance \:between \:town \:P and \:Q}}}}}}}$

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${\implies {\mathtt{ Distance \: covered\:by \:car + \: distance \:covered\:by\:van\: + 65 km.}}}$⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀ ⠀

${\implies {\mathtt{ D + D_{2} + 65 km}}}$

${\implies {\mathtt{ 192. 5 km + 165 km + 65 km}}}$

⠀⠀⠀⠀⠀⠀⠀ ⠀${\overline{\underline{\boxed{\mathtt{422.5 km}}}}}$

${\therefore{\mathtt{Distance \:between \:town \:P and \:Q\: is \:422.5 km}}}$

Answer 2

Explanation:

A car started from Town P and travelled towards Town Q at 70 km/h. At the same time a van started

from Town Q and travelled to Town P at 60 km/h. After 11/4 hours, they were 65 km apart, still travelling

towards each other.What is the distance between the two towns? After how many hours of travel would they cross each other?