Calculating time required with Mach and reported winds?

[BodhiWes]

I am having trouble figuring out the calculation for this question;

The following wind report relates to a WESTBOUND flight of a small business jet aircraft:
274045
How long would this aircraft take to cover a distance of 150 NM if it cruised at .83 Mach?

a) 31 mins
b) 25 mins
c) 20 mins
d) 17 mins

The answer is c) 20 mins. I feel like there is a simple calculation to this but I can't figure it out, nor can I find any examples through a Google search. Any help and guidance would be great. Thank so much.

[AuxBatOn]

I am having trouble figuring out the calculation for this question;

The following wind report relates to a WESTBOUND flight of a small business jet aircraft:
274045
How long would this aircraft take to cover a distance of 150 NM if it cruised at .83 Mach?

a) 31 mins
b) 25 mins
c) 20 mins
d) 17 mins

The answer is c) 20 mins. I feel like there is a simple calculation to this but I can't figure it out, nor can I find any examples through a Google search. Any help and guidance would be great. Thank so much.

A rule of thumb. Ever 0.1 Mach is 1 nauticaL mile a minute (or 60 kts) roughly. In this case, that’s 8.3 nautical miles a minute or 498 kts. With a 45 kts headwind, that’s 443 kts groundspeed. 150 nautical miles at 443 kts is 19.86 minutes...

[BodhiWes]

Thank you. How did you read the wind as a 45 kt headwind? I thought that was 270@40 -45C.

[AuxBatOn]

Thank you. How did you read the wind as a 45 kt headwind? I thought that was 270@40 -45C.

Sorry - I read the winds aloft quickly. 40 kts vs 45 kts. Add 5 to
The groundspeed that still gives you 19.65 minutes.

[BodhiWes]

Ok awesome. I really appreciate your help. Thanks so much.

[455tt]

I am having trouble figuring out the calculation for this question;

The following wind report relates to a WESTBOUND flight of a small business jet aircraft:
274045
How long would this aircraft take to cover a distance of 150 NM if it cruised at .83 Mach?

a) 31 mins
b) 25 mins
c) 20 mins
d) 17 mins

The answer is c) 20 mins. I feel like there is a simple calculation to this but I can't figure it out, nor can I find any examples through a Google search. Any help and guidance would be great. Thank so much.

We can do all of this on a pocket calculator with a square root key.

So we know that Mach No. or M = TAS/S, where S = the local speed of sound.

Since the free air temp is -40 deg. C we can calculate S based on 39 X (Sq. Rt. temp in Kelvin). Kelvin temp = deg. C + 273

Therefore, temp in Kelvin is 273 - 45 = 228 and S = 39 X (Sq. Rt. 228) = 589 kts

Now that we know S we can back calculate for the TAS. Since M = TAS/S, TAS = M X S = 589 X .83 = 489 kts

Finally, if we are cruising at 489 kts TAS into 40 kts headwind, our GS = 489 - 40 = 449 kts and our leg time for 150 NM is 20 minutes.