Hello. It's hard to know where to begin helping, when students don't show any initial efforts (or at least explain what they're confused about). There's a
guidelines notice that tells how to ask for help here. It's located at the top of the page after logging in (unless you closed it).
Start by assigning symbols to represent some unknown values.
Let d = distance from A to B
Let v = scheduled speed (what they've called "a constant speed")
Let t = scheduled time
You ought to have learned the relationship '
distance travelled equals constant speed times elapsed time'. Using our symbols, we can write:
d = v∙t
We're told that increasing the scheduled speed by 20% reduces the scheduled time by 1 hour. Hopefully, you already know how to increase a number by 20% (multiply it by 1.2). Therefore:
d = (1.2∙v)(t - 1)
Now substitute v∙t for d:
v∙t = (1.2∙v)(t - 1)
Solve this equation, to find t=6, by first dividing out v.
In other words, it takes 6 hr to drive from A to B, at constant speed v.
Under a different scenario, we're told that 36 min would be saved, if v were increased by 25% for the remainder of the trip after having driven 120km at speed v.
If a six-hour trip is completed 36 min sooner, how many hours did it take? In other words:
6 hr - 36 min =
?? hr
Determine
that number of hours.
Next, we don't know how much time it took to drive 120km at speed v, so let's introduce another symbol for that:
Let T = time required to drive 120km at speed v
v∙T = 120
Putting it all together:
6∙v = v∙T + 1.25∙v∙(
?? - T)
Solve for T.
Now that you know T, calculate v using v∙T=120
Then remember: The distance you're looking for is v∙t and you now have values for v and t.
There are other approaches, but you didn't show any work, so I went with
my first idea. How did I come up with my approach? By experimenting! That is, I made use of the basic relationship 'distance=velocity×time', I picked symbols for unknown quantities, I used the given scenarios relating these quantities and I tried writing equations and making substitutions, solving for what I could. After a little experimenting, I realized how to determine values for t and v. (Don't be afraid to try stuff; experimenting is good practice, and you can't really break anything by trying stuff.)
If you would like more help, please post your work or ask about the part(s) you don't understand. Cheers
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