SOLUTION: Natasha drove from Bedingfield to Portsmouth at an average speed of 100 km/h to attend a job interview. On the way back she decided to slow down to emjoy the scenery, so she drove

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Natasha drove from Bedingfield to Portsmouth at an average speed of 100 km/h to attend a job interview. On the way back she decided to slow down to emjoy the scenery, so she drove       Log On

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Question 895049: Natasha drove from Bedingfield to Portsmouth at an average speed of 100 km/h to attend a job interview. On the way back she decided to slow down to emjoy the scenery, so she drove at just 75 km/h. Her trip involved a total of 3.5 hours of driving time. What is the distance between Bedingfield and Portsmouth?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t%5B1%5D+ = time in hrs going
Let +t%5B2%5D+ = time in hrs coming back
Driving from Bedingfield to Portsmouth:
(1) +d=+100t%5B1%5D+
Driving back:
(2) +d+=+75t%5B2%5D+
and, also:
(3) +t%5B1%5D+%2B+t%5B2%5D+=+3.5+
--------------------------
By substitution:
(1) +75t%5B2%5D+=+100t%5B1%5D+
(1) +t%5B1%5D+=+%283%2F4%29%2At%5B2%5D+
Substitute (1) into (3)
(3) +%283%2F4%29%2At%5B2%5D+%2B+t%5B2%5D+=+3.5+
(3) +3t%5B2%5D+%2B+4t%5B2%5D+=+14+
(3) +7t%5B2%5D+=+14+
(3) +t%5B2%5D+=+2+
and
(3) +t%5B1%5D+=+3.5+-+t%5B2%5D+
(3) +t%5B1%5D+=+3.5+-+2+
(3) +t%5B1%5D+=+1.5+
------------------
(1) +d=+100t%5B1%5D+
(1) +d+=+100%2A1.5+
(1) +d+=+150+
The distance between Bedingfield and Portsmouth
is 150 km
--------------
check:
(2) +d+=+75t%5B2%5D+
(2) +d+=+75%2A2+
(2) +d+=+150+
OK