Question

Sydney started biking to the bookstore traveling 9 mph, after some time the bike got a flat so Sydney walked the rest of the way, traveling 7 mph. If the total trip to the bookstore took 7 hours and it was 57 miles away, how long did Sydney travel at each speed?

Answer 1

By bike= 4 hours

By walk= 3 hours

Explanation:

Given: Sydney travel by bike at 9 mph

Sydney travel by walk at 7 mph.

Total trip time= 7 hours

Distance to bookstore= 57 miles.

Lets assume the time spent travelling by bike be "x".

∴ Time spent travelling by walk is
`(7-x)`

Now, lets find the distance travelled on bike and by walk.

we know,
`Distance= speed* time`

∴ Distance by bike=
`9* x= 9x`

Distance by walk=
`7* (7-x)`

Using distributive property of multiplication.

∴ Distance by walk=
`49-7x`

Next, forming an equation for total distance travelled to find x.

⇒
`9x+ (49-7x)= 57\ miles`

Opening parenthesis

⇒
`9x+49-7x= 57`

⇒
`2x+49= 57`

Subtracting both side by 49

⇒
`2x= 8`

dividing both side by 2

⇒
`x= (8)/(2)`

∴
`x= 4\ hours`

Hence, time spent travelling on bike is 4 hours.

Subtituting the value x to find the time spent travelling by walk.

Times spent travelling by walk=
`7-4= 3\ hours`

hence, time spent travelling by walk= 3 hours