All Answers

+33666

As follows:

9876ⁿ (mod(100) = 9876 (mod(100)) = 76

Hence \(\Sigma_{n=1}^{99}9876^n (\mod(100) ) = 99*76 = 7524\)

AlanJun 25, 2020

+37193

You have to take into account the TIME at each speed.....the TIME to travel the same distance will be LONGER for 40 m/hr vs 60 m/hr so the AVERAGE will be weighted more toward the 40 m/hr ...

40 x t₁ = d d/40 = t1

60 x t₂= d d/60 = t2

2d/avg = t1 + t2 = d/40 + d/60

2d/avg = (3d+2d)/120

2/avg = 5/120

avg/2 = 120/5

avg = 240/5 = 48 m/hr

ElectricPavlovJun 25, 2020

+33666

Let the distance from A to B be L miles

time from A to B: t1 = L/40 hours

time from B to A: t2 = L/60 hours

Average speed for round trip = total distance/total time

so average speed = 2L/(t1 + t2) = 2L/(L/40 + L/60) = 2/(1/40 + 1/60) = 48 mph

AlanJun 25, 2020

+773

-1

nice explanation, itzme!

whymenotsmartJun 25, 2020

+134

the answere would be 2019, beacuse if you start solving it, you'll see the pattern (2/1 * 3/2 * 4/3 *...*2018/2017 * 2019/2018) so it will all simplify down to 2019.

ItzMeJun 25, 2020

+773

-1

40+60=100

100/2=50

should be 50 miles per hour, but remember, you have to also calculate the leftovers!

whymenotsmartJun 25, 2020

See Alan's answer here: https://web2.0calc.com/members/alan/?answerpage=751

Note: If you don't understand Alan's answer, there isn't anybody here, as far as I can tell, that understands it better than Alan. If you are looking for a "simpler" solution, I'm afraid you may have to find it somewhere else.

I suggest that you interact with your student friends and with your teacher to arrive at some sort of a solution that you will understand. Even WolframAlpha comes up with this message: "(unable to determine general term)" ! Good luck to you.

GuestJun 25, 2020

+773

-2

oh, lol

whymenotsmartJun 25, 2020

+37193

I initially read the Q incorrectly.....d'oh!