Question

A train leaves Miami at 5:00 PM. A second train leaves the same city in the same direction at 8:00 PM. The second train travels 90mph faster than the first. If the second train overtakes the first at 10:00 PM, what is the speed of each of the two trains?

Answer 1

$\bf \boxed \huge \mathfrak{ANSWER:}$

60mph and 150mph

$\red {STEP-BY-STEP \: \: VERIFICATION: }$

LET, THE SPEED OF FIFST TRAIN IS(x-90) mph AND OTHER IS (x )mph

TIME TAKEN BY FIRST TRAIN

$= 10: 00 - 5 : 000 \\ = 5hr$

TIME TAKEN BY SECOND TRAIN

$= 10 : 00 - 8: 00 \\ = 2hr$

NOW,

DISTACE=VELOCITY × TIME

SO,

DISTANCE OF FIRST TRAIN UPTO OVERTAKING POINT(D¹)

$= (x - 90)\times 5 \\ = (5x - 450) \: \: m$

SO,

DISTANCE OF SECOND TRAIN UPTO OVERTAKING POINT(D²)

$= (x) \times 2 \\ = 2x\: \: m$

WE KNOW,

$D {}^{1} =D {}^{2}$

OR,

$(5x - 450)\: \: m = ( 2x) \: \: m$

OR,

$3x = 180$

•°•

$x = 60 \: mph$

SO,

SPEED OF FIRST TRAIN

$= {60}mph$

SPEED OF SECOND TRAIN

$= v {}^{1} + 90mph \\ = 150mph$