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A journey of 192 km from …

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A journey of 192 km from Mumbai to Pune takes 2 hours less by a superfast train than that by an ordinary passenger train.If the average speed of the slower train is 16km/he less than that of the faster train. Determine their average speed ?

Posted by Ashwin Edakkara 6 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 1 month ago

Let speed of passenger train be x km/h
$\therefore$ speed of superfast train = (x + 16) km/h
By question, $T _ { \text { passenger } } = \frac { 192 } { x }$ and $\mathrm { T } _ { \text { superfast } } = \frac { 192 } { ( x + 16 ) }$
or, $\frac { 192 } { x } - \frac { 192 } { x + 16 } = 2$
or, $192 ( x + 16 ) - 192 x = 2 \left( x ^ { 2 } + 16 x \right)$
or, $192 x + 192 \times 16 - 192 x = 2 \left( x ^ { 2 } + 16 x \right)$
192x + 3072 - 192x $= 2 \left( x ^ { 2 } + 16 x \right)$ ( divide throughout by 2, we get,
96x + 1536 - 96x $= \left( x ^ { 2 } + 16 x \right)$
or x(x + 48) - 32(x + 48) = 0
or, (x - 32) (x + 48) = 0
or, x = 32 or - 48
Since speed can't be negative, therefore - 48 is not possible.
$\therefore$ Speed of passenger train = 32 km/h and Speed of fast train = 48 km/h

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This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

Few rules to keep homework help section safe, clean and informative.

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