person(1) traveled by vehicle(1) at an average speed of SPEED1 miles per hour.
Then, he(1) traveled by vehicle(2) at an average speed of SPEED2 miles per hour.
In total, he(1) traveled DIST miles for plural(TIME, "hour").
How many miles did person(1) travel by vehicle(1)? (Round to the nearest mile.)
round(DIST1)
d_vehicleVar(1) = round(DIST1)
miles
How many miles did person(1) travel by vehicle(2)? (Round to the nearest mile.)
round(DIST2)
d_vehicleVar(2) = round(DIST2)
miles
How many minutes did person(1) travel by vehicle(1)? (Round to the nearest minute.)
round(DIST1 / SPEED1 * 60)
t_vehicleVar(1) = round(DIST1 / SPEED1 * 60)
minutes
How many minutes did person(1) travel by vehicle(2)? (Round to the nearest minute.)
round(DIST2 / SPEED2 * 60)
t_vehicleVar(2) = round(DIST2 / SPEED2 * 60)
minutes
Remember that d = r * t
, or written another way, t = d / r
.
d_vehicleVar(1) =
distance that person(1) traveled by vehicle(1)
d_vehicleVar(2) =
distance that person(1) traveled by vehicle(2)
Total distance: d_vehicleVar(1) + d_vehicleVar(2) = DIST
Total time: t_vehicleVar(1) + t_vehicleVar(2) = TIME
t_vehicleVar(1) = (d_vehicleVar(1) / SPEED1)
and
t_vehicleVar(2) = (d_vehicleVar(2) / SPEED2)
Substitute the blue equations for:
(d_vehicleVar(1) / SPEED1) + (d_vehicleVar(2) / SPEED2) = TIME
Multiply the above equation by -1 * SPEED1:
-d_vehicleVar(1) - (SPEED1 / SPEED2) * d_vehicleVar(2) = -SPEED1 * TIME
Add the two orange equations for:
(SPEED2 - SPEED1 / SPEED2) * d_vehicleVar(2) = DIST - (SPEED1 * TIME)
Calculating all variables (and then rounding to the nearest integer):
d_vehicleVar(2) =
roundTo( 4 , DIST2 ) (round(DIST2))
miles
d_vehicleVar(1) =
roundTo( 4 , DIST1 ) (round(DIST1))
miles
t_vehicleVar(1) =
roundTo( 4 , DIST1 / SPEED1 * 60 ) (round(DIST1 / SPEED1 * 60))
minutes
t_vehicleVar(2) =
roundTo( 4 , DIST2 / SPEED2 * 60 ) (round(DIST2 / SPEED2 * 60))
minutes