A quarter of the distance = 640 / 4 = 160 miles
rest of the distance = 640 - 160 = 480 miles
Distance, speed, time formula:
s = d / t
If he did not make a rest he would travel:
t = 640 / s1 [ hours ]
where s1 = speed in a first quarter of the distance
t1 = d / s1 = 160 / s1
where t1 =time in a first quarter of the distance
time of a rest = 1.2 [ hours ]
New speed:
s2 = s1 + 20
New time = t2 = rest of the distance / new speed
t2 = 480 / ( s1 + 20 )
In order to arrive at the destination on time mean a trip will last:
640 / s1
how long it would take to travel at a constant speed to lasted s1
Total time:
t = 160 / s1 + 1.2 + 480 / ( s1 + 20 ) = 640 / s1
[ 160 ∙ ( s1 + 20 ) + 1.2 ∙ s1 ∙ ( s1 + 20 ) + 480 ∙ s1 ] / [ s1 ∙ ( s1 + 20 ) ] = 640 / s1
( 160 s1 + 3200 + 1.2 s1² + 24 s1+ 480 s1 ) / [ s1 ∙ ( s1 + 20 ) ] = 640 ∙ ( s1 + 20 ) / [ s1 ∙ ( s1 + 20 ) ]
( 1.2 s1² + 664 s1+ 3200 ) / [ s1 ∙ ( s1 + 20 ) ] = 640 ∙ ( s1 + 20 ) / [ s1 ∙ ( s1 + 20 ) ]
Multiply both sides by s1 ∙ ( s1 + 20 )
1.2 s1² + 664 s1 + 3200 = 640 ∙ ( s1 + 20 )
1.2 s1² + 664 s1 + 3200 = 640 s1 + 12800
Subtract 640 s1 + 12800 to both sides
1.2 s1² + 664 s1 + 3200 - 640 s1 - 12800 = 0
1.2 s1² + 24 s1 - 9600 = 0
Divide both sides by 1.2
s1² + 20 s1 - 8000 = 0
The solutions are:
s1 = - 100
and
s1 = 80
Speed can't be negative so:
s1 = 80 miles / hour
Total time:
t = 160 / s1 + 1.2 + 480 / ( s1 + 20 )
t = 160 / 80 + 1.2 + 480 / ( 80 + 20 )
t = 2 + 1.2 + 480 / 100
t = 2 + 1.2 + 4.8
t = 8 hours
A tourist has planned a trip to cover the distance of 640 miles, driving at some constant speed. However, when he already covered a quarter of the distance, he took a rest for 1.2 hours. Then, in order to arrive at the destination on time, he increased the speed by 20 mph. How long, actually, the trip lasted?
1 answer
1 answer