Question 1128381
{{{235/564+225/540}}}, in hours



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Ratio of distance to time, is speed.
D, distance; unit may be miles;
T, time; unit may be hours
R, "speed"


{{{D/T=R}}}, and the uni for R could be MILES per HOUR.


A couple of simple algebra steps:
{{{(D/T)T=RT}}}

{{{D=RT}}}

{{{D(1/R)=RT(1/R)}}}

{{{D/R=T}}}, a formula for time.


Look at the problem description.  Two different distances as part of a trip, and each distance at a different speed.


|  flies 235 miles with a constant speed of 564 mph |

The amount of time for this was {{{235(miles)*(1/564)(hours/miles)=(235/564)hours}}}.



| and another 225 miles with a constant speed of 540 mph.  |

This portion amount of time was  {{{(225/540)hours}}}.



The total amount of time was the sum:


{{{235/564+225/540}}}, in hours;

The rest is basic arithmetic.


Factorizing numerator and denominators completely:

{{{(5*47)/(2*2*3*47)+(3*3*5*5)/(2*2*3*3*3*5)}}}


Reduce EAch of them:

{{{5/12+5/12}}}


{{{10/12}}}


{{{highlight(5/6)}}}{{{highlight(hour)}}}


Change into minutes:

{{{(5/6)*(60(minutes/hour))}}}


{{{highlight(50*minutes)}}}